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.