Addressing "deep concern" over revelations by whistleblower Edward Snowden, an EU Council statement said the partnership between Europe and the US "must be based on respect and trust".
"A lack of trust could prejudice the necessary cooperation in the field of intelligence gathering," it added.
The EU summit in Brussels "unanimously" agreed to demand "a certain number of explanations" because "we know there will be other revelations", French President François Hollande said at a press conference after Thursday's meeting.
The aim is to "find an agreement on mutual relations before the end of the year", European Council president Herman Van Rompuy said.
He insisted that all 28 countries represented at the summit backed the move by Germany and France, despite reports that Britain, which is reported to have joined the US in spying on Italy to obtain data about underwater fibre-optic cables, was not keen to do so.
The summit stoped short at suspending talks over an EU-US free-trade agreement, as some officials had suggested.
Merkel opposed such a move, arguing, "When you leave the room you have to work out how to get back."
Hollande, who said that there was "deep concern among European citizens" on the matter, was right about the prospect of new revelations.
The NSA monitored the phones of 35 world leaders, according to Friday's Guardian newspaper, which reproduced a memo showing that an unnamed US official handed over 200 phone numbers, including 35 leaders of countries and that they were immediately "tasked".
Merkel suspected that she was being bugged after finding her mobile number written on a US document, according to Reuters news agency.
The US stopped short of denying that it had snooped on the German chancellor, although it said it is not doing so now and would not do so in the future.
"We are not going to comment publicly on every specified alleged intelligence activity," White House spokesperson Jay Carney said.