Germany and France are to spearhead a drive to try to force the Americans to agree new transatlantic rules on intelligence and security service behaviour in the wake of the Snowden revelations and allegations of mass US spying in France and tapping of the German chancellor Angela Merkel's mobile phone.

At an EU summit in Brussels that was hijacked by the furore over the activities of the National Security Agency in the US and Britain's GCHQ, the French president, François Hollande, also called for a new code of conduct agreed between national intelligence services in the EU, raising the question of whether Britain would opt to join in.

Shaken by this week's revelations of NSA operations in France and Germany, EU leaders and Merkel in particular warned that the international fight against terrorism was being jeopardised by the perception that mass US surveillance was out of control.

The leaders "stressed that intelligence-gathering is a vital element in the fight against terrorism", a summit statement said. "A lack of trust could prejudice the necessary co-operation in the field of intelligence-gathering."

Merkel drove the point home: "We need trust among allies and partners. Such trust now has to be built anew … The United States of America and Europe face common challenges. We are allies. But such an alliance can only be built on trust."

Privately, according to senior sources who witnessed the two-hour discussion of intelligence snooping on Thursday evening, Merkel told the other leaders that the issue at stake was not that her mobile phone may have been tapped by the Americans, but that it represented "the phones of millions of European citizens".

While conceding that intelligence services everywhere might be prone to behaving badly, Hollande dismissed suggestions that the Americans were merely operating as other security services also did. He complained that the revelations by the US whistleblower, Edward Snowden, showed a level of eavesdropping and data gathering that took place nowhere in Europe and was unique to the US agency.

A delegation of nine MEPs will travel to Washington on Monday for a three-day visit, during which they will press senior US government and intelligence officials for answers on allegations of widespread spying by the US, and explore "possible legal remedies for EU citizens" resulting from the alleged surveillance.

Separately, the German government said on Friday that a group of senior officials including the heads of its foreign and domestic intelligence agencies would travel to the US "shortly" for talks at the White House and with the NSA.

The White House spokesman Jay Carney said the Obama administration was discussing Germany's concerns "through diplomatic channels at the highest level".

It is plain that the French and the Germans want to limit the damage from the NSA furore, but also hope to engage the Americans to rein in their activities. They set a deadline of the end of the year for results. The statement said other countries could join the negotiations, leaving the door open for British participation.

Given the role of GCHQ in the mass surveillance, Cameron found himself the target of veiled criticism at the summit, according to witnesses. Merkel complained that Britain enjoyed a privileged position with the Americans because it is the only EU member in the "Five Eyes Club" – the intelligence-sharing arrangement linking the US, the UK, Canada, Australia and New Zealand.

Senior EU security officials suspect that Berlin may seek to exploit the crisis to gain admission to, or at least greater co-operation with, the Five Eyes pact.

Cameron, sources said, responded to the critical remarks by stressing that under his premiership the shared intelligence with the four other countries had resulted in several terrorist plots being foiled, with countless lives saved.

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

Despite US efforts to placate Merkel – including a phone call with the US president, Barack Obama, on Wednesday – she has refused to conceal her anger.

Merkel briefed the other leaders in some detail on the 20-minute conversation with Obama, sources said, adding that several participants commented that they thought the US leader was "embarrassed".

The European anger and frustration was directed at a US agency seen to be out of control and beyond appropriate scrutiny rather than being aimed at Obama.

The latest confidential memo provided by Snowden reveals that the NSA encourages senior officials in its "customer" departments – such as the White House, state department and the Pentagon – to share their Rolodexes so that 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 has been named. These were immediately "tasked" for monitoring by the NSA.