The heads of German foreign and domestic intelligence would hold talks with the White House and the National Security Agency (NSA), a government spokesperson said.
Earlier, Germany and France said they want the US to sign a no-spy deal by the end of the year.
EU leaders at a Brussels summit have warned a lack of trust could harm the fight against terrorism.
As well as the bugging of Angela Merkel’s phone, there are claims the NSA has monitored millions of telephone calls by both German and French citizens.
Spain on Friday followed Germany and France in summoning the US ambassador to explain reports of spying on the country. Italy has also expressed anger at reports it too has been spied on.
US state department spokesperson Jen Psaki acknowledged that the revelations – most of them sourced to former NSA worker Edward Snowden – have “posed a moment of tension with some of our allies”.
“We are having discussions with those allies, those will continue, as is evidenced by the German delegation that will be coming here in the coming weeks,” she said.
Jen Psaki also said a review of US intelligence gathering, called for by President Barack Obama, would look at how it affects foreign policy.
The “high level group of outside experts… will consider as part of this how we can maintain the public’s trust, how the surveillance impacts our foreign policy, particularly in an age when more and more information is becoming public,” she said.
On Friday, the NSA website itself was inaccessible for several hours, with numerous hacking groups claiming credit for the service outage.
The issue was later put down to “an internal error that occurred during a scheduled update”, NSA spokeswoman Vanee Vines said.
“Claims that the outage was caused by a distributed denial of service attack are not true.”
German government spokesman Georg Streiter did not give a date for the intelligence chiefs’ trip to Washington but said it was being arranged with “relatively short notice”.
“What exactly is going to be regulated, how and in what form it will be negotiated and by whom, I cannot tell you right now,” Georg Streier told reporters.
“But you will learn about it in the near future because we have created some pressure to do this speedily.”
Angela Merkel made clear her anger at the allegations, which emerged in the German media, when she arrived in Brussels on Thursday for the EU summit.
The German chancellor told reporters after the first day that “once the seeds of mistrust have been shown it doesn’t facilitate our co-operation… it makes it more difficult”.
Angela Merkel said they would be pressing for 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”.
At a news conference on Friday Angela Merkel said both Berlin and Paris would, separately, be pressing Washington for a deal that is “clear-cut, in line with the spirit of an alliance”.
French President Francois Hollande said the aim of the initiative “is about knowing about the past and setting a framework for the future and putting an end to monitoring mechanisms that are not controlled”.
Observers say they may be seeking an arrangement similar to the “Five Eyes” intelligence-sharing agreement the US has had with Britain, Australia, New Zealand and Canada since just after World War II.
A statement from EU leaders on Friday said the recent intelligence issues had raised “deep concerns” among European citizens.
The leaders “underlined the close relationship between Europe and the USA and the value of that partnership,” and “stressed that intelligence-gathering is a vital element in the fight against terrorism.”
But, the statement went on: “A lack of trust could prejudice the necessary cooperation in the field of intelligence-gathering.”
There are reports that the NSA has monitored the phones of 35 world leaders.
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