(CNN) -- "Trust needs to be rebuilt."
That's what German Chancellor Angela Merkel firmly asserted early Friday -- as she had the previous day -- in the wake of reports the U.S. National Security Agency had eavesdropped on her cell phone.
This claim and others that she and other world leaders have been spied on had "severely shaken" relationships between Europe and the United States, the German leader said.
"Obviously, words will not be sufficient," Merkel said in the wee hours Friday at a summit of European Union leaders. "True change is necessary."
Talk of the NSA's reported spying on Germany and other allies dominated Merkel's news conference in Brussels, Belgium. It illustrated the anger over this story in Europe and the challenges facing Washington because of it.
The Chancellor insisted she isn't the only one concerned; other European leaders, she said, voiced similar sentiments during the first day of the summit Thursday.
Her comments echoed some she'd made upon arriving Thursday in Belgium, when she said that discussions of "what sort of data protection do we need and what transparency is there" should now be on European leaders' agenda.
"We need trust,..." she said. "Spying among friends is never acceptable."
U.S. President Barack Obama understands it's a "necessity" for change from his nation's perspective, according to Merkel, who spoke with the American leader on Wednesday after Germany's government said it had information the United States might have monitored her phone.
She told Obama that eavesdropping among friends is "never acceptable, no matter in what situation," she said.
On Thursday, White House spokesman Jay Carney repeated what he said Wednesday -- that Obama assured Merkel that the United States is not monitoring and will not monitor her communications.
And in a USA Today op-ed published online Thursday night, Obama's homeland security and counterterrorism adviser Lisa Monaco conceded that recent "disclosures have created significant challenges in our relationships." To address them, the President has ordered a "review (of) our surveillance capabilities, including with our foreign partners," she wrote.
"We want to ensure we are collecting information because we need it and not because we can," said Monaco.
The German allegation comes in the same week that French daily newspaper Le Monde reported claims the NSA intercepted more than 70 million phone calls in France over 30 days.
And The Guardian newspaper -- citing a document obtained from U.S. government contractor-turned-whistleblower Edward Snowden -- reported Thursday that the NSA monitored phone conversations of 35 world leaders. The confidential memo is from 2006, which is before Obama became president. None of the monitored world leaders is identified.
The phone numbers were among 200 handed over to the NSA by a U.S. official, the memo states. Others were encouraged to share their "rolodexes" with the agency, according to the document, even though tracking until then had yielded "little reportable intelligence."
Like Carney, NSA spokeswoman Caitlin Haden refused "to comment publicly on every specific intelligence activity."
"As we have made clear," she added, "... the United States gathers foreign intelligence of the type gathered by all nations."
European leaders push for data protection
It's not clear how well such explanations will be received by Washington's allies in Europe elsewhere, or how significantly it has and will continue to affect the European Council meeting.
The two-day summit was supposed to focus on the digital economy and economic and social policy issues, as well as concerns about EU migration after a recent shipwreck off an Italian island in which hundreds of migrants from Africa died.
But French Prime Minister Jean-Marc Ayrault told the French National Assembly on Tuesday that France would ask for the question of electronic surveillance to be added to the agenda.
The EU leaders were expected to discuss data protection issues as part of their debate on the digital economy.
Viviane Reding, vice president of the European Commission, called for EU nations to commit to adopting a data protection law in light of the recent spying scandals.
"Data protection must apply to everyone -- whether we are talking about citizens' e-mails or Angela Merkel's mobile phone," she said. "We now need big European rules to counter big fears of surveillance.
"At the summit today, Europe's heads of state and government must follow words with action: They should commit to adopting the EU Data Protection Reform by spring 2014. This would be Europe's declaration of independence. Only then can Europe credibly face the United States."
Even before the latest allegations, Germany and other nations had expressed concerns about alleged U.S. spying after Snowden -- a former National Security Agency contractor -- leaked classified information about American surveillance programs.
German news magazine Der Spiegel reported in June that leaks from Snowden detailed how the agency bugged EU offices in Washington and New York, and conducted an "electronic eavesdropping operation" that tapped into an EU building in Brussels.
Merkel spoke with Obama by phone in July about allegations that the United States was conducting surveillance on its European allies.
Merkel made it clear that if the information about the U.S. having monitored her phone were true, it would be "completely unacceptable," spokesman Steffen Seibert said of Wednesday's call with Obama.
A spokesman for David Cameron declined to answer questions Thursday about whether the British Prime Minister's phone had been tapped by the United States, following Germany's suspicion about U.S. monitoring of Merkel's cell phone.
"I am not going to comment on matters of security or intelligence," the spokesman told reporters at a regular briefing.
Ayrault: 'Shocking' claims
Ayrault described the report of widespread spying by the NSA on French calls as "worrying" and "shocking," saying that security should not be guaranteed at the price of a loss of freedom.
However, U.S. Director of National Intelligence James Clapper suggested that the claims made by Le Monde were false.
The articles "contain inaccurate and misleading information regarding U.S. foreign intelligence activities," a written statement from his office said Tuesday. It added that the United States does gather intelligence of "the type gathered by all nations."
Nonetheless, the allegations prompted a flurry of diplomatic activity this week between the United States and France.
Obama and French President Francois Hollande spoke about the claims Monday.
"The President and President Hollande discussed recent disclosures in the press -- some of which have distorted our activities and some of which raise legitimate questions for our friends and allies about how these capabilities are employed," a White House statement said.
"The President made clear that the United States has begun to review the way that we gather intelligence, so that we properly balance the legitimate security concerns of our citizens and allies with the privacy concerns that all people share."
Hollande's office said the President expressed his "deep disapproval with regard to these practices" to Obama and that such alleged activities would be unacceptable between allies and friends.
The two Presidents agreed that French and American intelligence services would cooperate on investigating the report, according to the statement from the French President's office.
French Foreign Minister Laurent Fabius and U.S. Secretary of State John Kerry also met Tuesday to discuss the claims. The U.S. ambassador to France, Charles Rivkin, was summoned to the French Foreign Ministry in Paris on Monday to discuss the alleged spying.
Claims of U.S. spying, resulting from leaks by Snowden, have also soured U.S. relations with Mexico and Brazil.
Der Spiegel recently published allegations, citing Snowden as its source, that the U.S. National Security Agency "systematically" eavesdropped on the Mexican government and hacked the public e-mail account of former Mexican President Felipe Calderon.
CNN's Greg Botelho, Bharati Naik, Chris Williams, Claudia Otto, Stephanie Halasz, Alexander Felton and Michael Martinez contributed to this report.