Washington (CNN) -- President Barack Obama and political leaders from both parties stressed resolve and unity Wednesday after a day of violence in Arab Spring countries killed four American diplomats.
Meanwhile, GOP presidential challenger Mitt Romney and other Republicans harshly criticized the president's foreign policy as weak and conflicted.
The violence on Tuesday -- the 11th anniversary of the 9/11 terrorist attacks by al Qaeda on the United States -- included an attack that killed Ambassador Chris Stevens and three other diplomats in Benghazi, Libya, as well as protesters assaulting the U.S. Consulate there and the American embassy in Egypt.
Demonstrations over an anti-Islam video on a U.S. website spread Wednesday to Sudan, and officials warned of possible street protests in Afghanistan after midday prayers on Friday.
Obama, flanked by Secretary of State Hillary Clinton, hailed the service of Stevens and the other slain diplomats and promised to go after those responsible for their killings.
At the same time, the president stressed that U.S. support would continue for the democratic aspirations expressed by Arab Spring uprisings in Libya and Egypt, and that American values of religious tolerance and freedom should be followed around the world.
"We will not waver in our commitment to see that justice is done for this terrible act. And make no mistake, justice will be done," Obama said in the White House Rose Garden.
Referring to the video being promoted on anti-Islam websites in the United States, Obama said, "We reject all efforts to denigrate the religious beliefs of others."
"But there is absolutely no justification for this type of senseless violence. None," Obama said. "The world must stand together to unequivocally reject these brutal acts."
Obama later ordered U.S. flags flown at half-staff in memory of the victims before departing the White House for a campaign event on Wednesday night in Las Vegas. Press secretary Jay Carney said the president called the widow of Foreign Service information management officer Sean Smith and the parents of slain ambassador Chris Stevens.
In her own statement earlier, Clinton asked, "How could this happen in a country we helped liberate, in a city we helped save from destruction?"
"This question reflects just how complicated and at times how confounding the world can be," she said. "But we must be clear-eyed even in our grief. This was an attack by a small and savage group, not the people or government of Libya."
A joint statement by hawkish veteran Sens. John McCain of Arizona, Lindsey Graham of South Carolina and Joe Lieberman of Connecticut also condemned the attacks and called for justice while also expressing support for the mission in both Libya and Egypt.
"Despite this horrific attack, we cannot give in to the temptation to believe that our support for the democratic aspirations of people in Libya, Egypt, and elsewhere in the broader Middle East is naive or mistaken," said the statement by the senators, who have been strong critics of Obama for what they have called an unassertive foreign policy.
"We cannot resign ourselves to the false belief that the Arab Spring is doomed to be defined not by the desire for democracy and freedom that has inspired millions of people to peaceful action, but by the dark fanaticism of terrorists," they said.
McCain, the Republican presidential candidate against Obama in 2008, praised Clinton's statement on Twitter, saying it provided "just the right message and tone."
Romney, however, sharply criticized the administration on Wednesday, saying the U.S. response amounted to sending "mixed messages" on American values and foreign policy to the rest of the world.
"I think President Obama has demonstrated a lack of clarity as to a foreign policy," Romney said in Jacksonville, Florida, continuing a line of criticism his campaign began late Tuesday when he issued a statement that labeled the U.S. response to attacks on the Cairo embassy as "disgraceful."
"I think it is a terrible course for America to stand in apology for our values," Romney said of a statement issued by the embassy in Cairo that condemned the anti-Islam video that fomented protests outside the compound. "When our grounds are being attacked and being breached ... the first response of the United States must be outrage at the breach of the sovereignty of our nation. And apology for America's values is never the right course."
Although Romney said the statement was released after the violence at the embassy, in fact it was released hours earlier.
Romney said the White House later attempted to distance itself from the embassy statement, sending a conflicting message on foreign policy at a time when resolve and clarity were needed, and he made clear he believed the responsibility rested with Obama.
"The president takes responsibility not just for the words that come from his mouth but also from his ambassadors, from his administration, from his embassies, from his State Department," Romney said, adding: "They clearly sent mixed messages to the world. ... The statement that came from the administration was a statement which is akin to apology and I think was a severe miscalculation."
The president and other Democrats quickly fired back that the former Massachusetts governor's comments were inappropriate and misguided.
"There's a broader lesson to be learned here. Gov. Romney seems to have a tendency to shoot first and aim later." Obama told "60 Minutes" correspondent Steve Croft. "And as president one of the things I've learned is you can't do that. It's important for you to make sure that the statements that you make are backed up by the facts and that you've thought through the ramifications before you make them."
Former presidential candidate John Kerry also criticized Romney.
"They demonstrate an insensitivity and a lack of judgment about what is happening right now," the Senate Foreign Relations Committee chairman told CNN, adding: "I don't think he knows what he is talking about, frankly."
However, other Republicans including Romney's running mate in November, conservative Rep. Paul Ryan, joined in the criticism of the president.
Ryan told a campaign event in De Pere, Wisconsin, that the U.S. president must always "speak with a singular voice representing our principles and our values."
"If you show weakness, if you show moral equivocation then foreign policy adventurism among our adversaries will increase," he added, without mentioning Obama's name. "We do not want a world climate where our adversaries are so tempted to test us and our allies are worried about trusting us, and that is unfortunately the path that we are on right now."
Another conservative Republican, House Armed Services Committee Chairman Buck McKeon of California, made specific reference to Obama in a statement.
"Again and again under President Obama, we have met threats and thugs with apologies and concessions," McKeon said. "Unsurprisingly, these mobs aren't satisfied with apologies anymore, they have clearly been escalating the offensive in the war of ideas for some time. Is it any wonder that events spun out of control and that American lives were lost?"
Blog posts on the conservative website Tea Party Nation sought to equate the current situation to the fall of the U.S. Embassy in Iran that helped doom the 1980 re-election bid of former Democratic President Jimmy Carter.
Wednesday's campaign shift to foreign policy comes after months of concerted focus on jobs and the economy, especially by the Romney campaign in its effort to frame the vote as a referendum on Obama's handling of the nation's sluggish economic recovery.
Romney generally makes little mention of foreign policy on the stump, and was criticized for not mentioning the war in Afghanistan during his speech accepting the GOP nomination at last month's Republican National Convention.
The latest CNN/ORC International survey released earlier this week showed Obama with a 54%-42% advantage over Romney on foreign policy.
On Tuesday night, when only one of the diplomats in Libya was known to have been killed, Romney's campaign issued a statement in which he condemned both the assault on the embassy in Cairo and what he called the weak U.S. response.
"It's disgraceful that the Obama administration's first response was not to condemn attacks on our diplomatic missions, but to sympathize with those who waged the attacks," the Romney statement said, referring to the initial Cairo embassy statement that was released before protesters stormed the compound.
The embassy statement had said it "condemns the continuing efforts by misguided individuals to hurt the religious feelings of Muslims -- as we condemn efforts to offend believers of all religions."
"Respect for religious beliefs is a cornerstone of American democracy," the embassy statement continued. "We firmly reject the actions by those who abuse the universal right of free speech to hurt the religious beliefs of others."
Later, Clinton issued a statement that said anger over the film did not justify the violence.
"The United States deplores any intentional effort to denigrate the religious beliefs of others," Clinton wrote. "Our commitment to religious tolerance goes back to the very beginning of our nation. But let me be clear: There is never any justification for violent acts of this kind."
Romney's statement on Tuesday night originally had a 12 midnight embargo, apparently to stick to his previously stated intention to avoid overt politicking on the 9/11 anniversary. The campaign then lifted the embargo before midnight.
Obama's campaign responded quickly, saying Romney was using Middle East events for political gain.
"We are shocked that, at a time when the United States of America is confronting the tragic death of one of our diplomatic officers in Libya, Gov. Romney would choose to launch a political attack," Obama campaign press secretary Ben LaBolt wrote.
On Wednesday, legislators sounded united in their calls for justice and continued efforts to help bring peaceful democratic transitions in Libya, Egypt and elsewhere.
"I have seen this amateurish and stupid video, and there is nothing in it -- despite the fact that it is deliberately provocative -- that could ever justify the murder of these innocent people," said Rep. Keith Ellison, D-Minnesota, the only Muslim U.S. lawmaker.
Senate Republican leader Mitch McConnell of Kentucky said he supported "employing every available tool at our disposal to ensure the safety of Americans overseas and to hunt down those responsible for those attacks."
"Yesterday we commemorated the anniversary of the attacks of September 11," he added, "and today we are reminded that brave Americans serve us every day at the risk of their own lives."
CNN's Peter Hamby, Elise Labott, Kate Bolduan,Ted Barrett, Brianna Keilar, Dan Lothian, Elise Labott, Rachel Streitfeld, Jill Dougherty, Ashley Killough, Barbara Starr and Lesa Jansen contributed to this report.