Deputy Prime Minister John Prescott has denied saying the Bush administration had been "crap" on the Middle East road map - the plan for peace in the region.
Mr Prescott made "an honest and good point", Mr Cohen said
Labour MP Harry Cohen said the remark came during a private, "robust" meeting on Tuesday with fellow Labour MPs.
Mr Prescott said it was an inaccurate report of a private conversation.
The White House said President George W Bush had been called worse, stressing Tony Blair was UK Prime Minister, and he and Mr Bush worked closely together.
President Bush's press secretary Tony Snow, asked about the reported comments, insisted negative remarks were part of the burden of leadership.
They were said to have been made at talks with Muslim MPs and other Labour MPs with constituencies representing large Muslim communities.
Asked about Mr Prescott's denial, Mr Cohen told the BBC he did not think it was a "gaffe" by the deputy PM and that Mr Prescott should not be embarrassed.
Mr Cohen said he believed Mr Prescott's comment had been "an honest and good point, well made".
Asked why Mr Prescott might deny it, Mr Cohen - whose constituency includes areas of east London where some terror raids took place last week - claimed it might be politically expedient "not to upset the Americans".
He said he thought many of his fellow MPs and the wider population would agree that more should have been done by the US in pushing forward the Middle East road map in recent years.
Mr Cohen said Mr Prescott's "crap" comment had been specific to the US efforts on the road map.
It was not a view of President Bush generally, the Bush administration as a whole, or the Bush administration's general Middle East policy, he added.
"That's my distinct memory, that he did use that word, quite properly in the context of the road map," he told BBC News 24.
"We had a robust discussion about foreign affairs. Right at the end of the meeting he said: 'Well, you're going to speak to the press - take from it what you want.'
"I did, and I think that's quite legitimate."
He said Mr Prescott claimed he had only supported the Iraq war "because they were promised the road map".
Mr Cohen said Mr Prescott's other reported comment - calling Mr Bush a "cowboy" - was a joke related to his own recent difficulties over a cowboy outfit gift he was given last year.
'Cheering him on'
Colin Brown, who is the deputy prime minister's biographer, said that this was "the type of language" used by Mr Prescott.
"It's a shorthand, it's very pithy, it's not diplomatic, and I hope that he doesn't get into any diplomatic hot water about it," he told BBC News 24.
"But the fact is, a lot of people are cheering him on."
Former ministers were "right behind him on this", Mr Brown added, and the deputy prime minister had "never been more popular than he is now" as a result.
For the Lib Dems, Norman Lamb, said: "John Prescott does not always use the most appropriate language, but if these reports are to be believed then his instincts on the Middle East are certainly preferable to Tony Blair's."
Mr Prescott has been Tony Blair's deputy since he came to power in 1997. Mr Blair is on holiday at the moment, leaving Mr Prescott in charge of the government.