Assistant Secretary of State Victoria Nuland has already apologised to EU officials for the remark.
A spokeswoman for EU foreign policy chief Catherine Ashton said on Friday that she would not comment on leaked alleged telephone conversations.
Washington has been in damage-control mode ever since a video surfaced on YouTube in which Nuland vents her frustration over the mass protests in Ukraine. The comments were made on Tuesday to Geoffrey Pyatt, the US ambassador to Kiev, but not widely reported until Thursday.
"So that would be great, I think, to help glue this thing and have the UN help glue it, and, you know, fuck the EU," Nuland wais recorded as saying.
Nuland told reporters in Kiev: "I won't comment. This is a private diplomatic conversation."
In Berlin, Angela Merkel's spokeswoman said, "The chancellor considers the remark absolutely unacceptable."
Spokeswoman Christiane Wirtz said the German leader also believed the EU's foreign policy chief, Catherine Ashton, had been doing a fine job dealing with the crisis in Ukraine.
"Bugging gets just so messy," a German Foreign Ministry spokesman joked, in an oblique reference to admissions last year that US spies had listened in on Merkel's mobile phone calls.
Asked by reporters if this meant Germany was certain Nuland's conversation had been bugged by Russia, he said they should consult what was said at a US State Department news conference.
Russia and the US have been at loggerheads over Ukraine, accusing each other of interfering in the country's internal affairs, and officials in Washington pointed out that the YouTube post was first cited by Russian Twitter users.
US State Department spokeswoman Jen Psaki did not directly accuse Russia of recording and leaking the telephone call, but spoke of "a new low in Russian tradecraft".
White House spokesman Jay Carney said the video was first noted and tweeted by the Russian government. "I think it says something about Russia's role," he said.
Carney was referring to Dmitry Loskutov, an aide to Deputy Prime Minister Dmitry Rogozin, who had tweeted a link to the video early on Thursday.
In Moscow analysts were guessing on who was to blame for the leak. Andrei Soldatov, a leading Russian security expert, said that both Russian and Ukrainian intelligence could be responsible for the recording because of their close ties.
But the Ukrainian Security Service (SBU), had an advantage over the Russians, he said.
"The SBU's surveillance systems are more intrusive because they have less restrictive laws than Russia," Soldatov told dpa.
The audio leak became widely known after being reported in the English-language Kyiv Post newspaper late Thursday, coinciding with a visit by Nuland to the Ukrainian capital.
In a light-hearted reaction, Pyatt posted a photo on Twitter of himself, Nuland and Ukrainian opposition leaders around an iPad and addressed it to Liskutov, whom he referred to by the short form of his first name Dmitry: "Enjoying Dima's tweet here in Kyiv."
However, Loskutov denied being the original source for the leak. "I was just monitoring 'the internets' while my boss was off to a meeting with the Chinese leader," he said on Twitter.
The YouTube post, called "Puppets of the Maidan," after the Kiev square that has been occupied by protesters for more than two months, has Russian subtitles.
It was uploaded by an anonymous user called Re Post and garnered more than 200,000 views by Friday afternoon.
Acknowledging Nuland's apology, European Parliament President Martin Schulz said that "the term 'diplomat' and her choice of words actually stand in contradiction to one another."