The French and German governments have demanded talks with the US by the end of the year as the row over the spying activities of the US National Security Agency intensifies.

Their calls follow reports that the German chancellor, Angela Merkel, had her phone monitored by the NSA and reports that the agency eavesdropped on calls made by members of the French administration.

The revelations are threatening to create a major rift between the US and its European allies. The former Belgian prime minister and leader of the Group of the Alliance of Liberals and Democrats for Europe in the European parliament, Guy Verhofstadt, told BBC Radio 4's Today programme that such activities had to be curtailled. "There is no reason to spy on Angela Merkel. It's a real scandal," he said. "A new agreement is needed between the EU and the US; this cannot continue.

Others, however, were less shocked by recent reports. "I can't believe anyone is terribly surprised," Kurt Volker, a former US ambassador to Nato, told the same programme. Volker said every government tried to collect the best possible information, adding: "As a government official for many years I assumed that my cellphone and email account were susceptible to spying."

The controversy deepened on Thursday when the Guardian revealed the NSA had monitored the phone conversations of 35 world leaders after being given the numbers by an official in another US government department. The latest claims, which emerged from a classified document provided by the whistleblower Edward Snowden, have further overshadowed this week's EU summit in Brussels.

Despite US efforts to placate Merkel – including a phonecall made by the US president, Barack Obama, on Wednesday – she has refused to conceal her anger over the issue. "We need trust among allies and partners," Merkel told reporters in Brussels on Thursday. "Such trust now has to be built anew. This is what we have to think about."

Although the US and Europe were allies facing the same challenges, she said, "such an alliance can only be built on trust. That's why I repeat again: spying among friends, that cannot be." She added: "It's become clear that for the future, something must change – and significantly.

"We will put all efforts into forging a joint understanding by the end of the year for the co-operation of the [intelligence] agencies between Germany and the US and France and the US, to create a framework for the co-operation."

Her sentiments were echoed by the French president, François Hollande. "What is at stake is preserving our relations with the United States," he said. "They should not be changed because of what has happened. But trust has to be restored and reinforced."

The latest confidential memo provided by Snowden reveals that the NSA encourages senior officials in its "customer" departments – such the White House, State and the Pentagon – to share their "Rolodexes" so the agency can add the phone numbers of leading foreign politicians to their surveillance systems.

The document notes that one unnamed US official handed over 200 numbers, including those of the 35 world leaders, none of whom is named. These were immediately "tasked" for monitoring by the NSA.

After Merkel's allegations became public, the White House press secretary, Jay Carney, issued a statement that said the US "is not monitoring and will not monitor" the German chancellor's communications. But that failed to quell the row, as officials in Berlin quickly pointed out that the US did not deny monitoring her phone in the past.

Earlier, it was reported that the US had denied ever spying on the British prime minister, David Cameron. Caitlin Hayden, a spokesman for the National Security Council, told the Daily Telegraph: "We do not monitor PM Cameron's communications."

Asked if the US had ever spied on Cameron in the past, she replied: "No."

The prime minister's official spokesman refused to comment, saying: "I'm not going to comment on matters of security or intelligence."

Britain and the US – along with Canada, Australia and New Zealand – are members of the so-called Five Eyes group, who share signals intelligence and are supposed not to spy on each other.