The remarks follow a week-long episode where leaked DNC emails showed Democratic officials giving preferential treatment to Hillary Clinton. The emails inflamed supporters of her primary opponent, Bernie Sanders, during the Democratic Party's national convention, which led to widespread protest and the ousting of DNC Chairwoman Debbie Wasserman Schultz.
Asked about potential consequences for the hack, the White House described "a full range of options available to us in the government."
"That includes economic sanctions out of Department of Treasury. That includes a number of law enforcement measures that Department of Justice has announced and has taken action on," said spokesman Eric Schultz.
"The United States isn't going to pull any punches in terms of our response," he said.
The FBI said Monday they were investigating the hack. FBI Director James Comey also said Wednesday morning that some of the main players behind cyber threats are nation states like China, Russia, Iran and North Korea, but he did not comment on this specific case.
President Barack Obama said "anything's possible" when asked by NBC in an interview that aired Wednesday whether Russian President Vladimir Putin was trying to interfere with US presidential politics. Obama also noted that Republican presidential nominee Donald Trump has repeatedly praised Putin.
Trump said Wednesday that suggestions that Russia orchestrated the DNC hack to help his campaign were "a deflection." In one breath, the Republican nominee suggested that Russia might not be responsible and in the next he called on Russia to help his campaign by accessing and releasing Clinton emails from her tenure as secretary of state.
As Republican Party leaders such as House Speaker Paul Ryan were calling for Russia to "stay out of this election," according to Ryan spokesman Brendan Buck, Trump was speaking at a Florida press conference and saying, "Russia, if you're listening, I hope you're able to find the 30,000 e-mails that are missing."
"I think you will probably be rewarded mightily by our press," Trump said in Miami.
The idea that Russia might be acting to help him "is so farfetched, it's so ridiculous," Trump said. "Honestly, I wish I had that power. I'd love to have that power."
The House intelligence committee's senior Democrat, California Rep. Adam Schiff, charged that Trump's comments showed "staggeringly poor judgment."
"That he would issue this call at the same time that Russia may have already hacked the Democratic National Committee and released emails in order to boost Trump's own candidacy is all the more breathtakingly irresponsible," Schiff said in a statement.
When asked about Donald Trump's comment, House Speaker Paul Ryan's spokesman Brendan Buck deflected and focused instead on Russia.
"Russia is a global menace led by a devious thug. Putin should stay out of this election," Buck said.
Trump went on to emphasize that "nobody even knows" if responsibility lies with Russia. He suggested that another country or even Clinton campaign manager Robby Mook might be the indirect source of the hack. "It's probably China, or it could be somebody sitting in his bed," Trump said.
And while he denied any connection to Putin, saying, "I never met Putin, I don't know who Putin is," Trump added, "There's nothing that I can think of that I'd rather do than have Russia friendly as opposed to the way they are right now."
Trump returned to a favorite theme, arguing that, "Putin and the leaders throughout the world have no respect for our country anymore and they certainly have no respect for our leader."
The Kremlin has dismissed accusations that its behind the hack, calling them "made-up horror stories."