Mr Olmert had sought to defuse the political crisis caused by the investigation by presenting a 'business as usual' image, continuing his scheduled programme of visits and meetings.

But the announcement by the Israeli police that witnesses would be sought in the United States raises the possibility of new lines of inquiry that could further undermine Mr Olmert.

It was evidence given to an Israeli court last week from an American businessman that sparked the most serious challenge to Mr Olmert's two year old premiership.

In that evidence, Morris Talansky told how he gave about £100,000 to Mr Olmert over a 15 years, often in the form of dollar notes stuffed into envelopes, without receipts and scantily accounted for.

It prompted the leader of the Labour party, Ehud Barak, the largest coalition partner of Mr Olmert's Kadima party, to call for the prime minister to stand down.

It also led to his own Kadima party colleague and foreign minister, Tzipi Livni, to publicly hint the time has come for him to go.

But if nothing else, Mr Olmert is a fighter and he has sought to rebuff both challenges, visiting Mahmoud Abbas, the moderate Palestinian leader, for a scheduled meeting on Monday.

Israeli police sources said detectives from the National Fraud Unit will travel to the US "in the coming days" to continue the criminal investigation into Mr Olmert.

The National Fraud Unit will focus on finding the additional donors who sent Mr Talansky funds to pass on to Mr Olmert, according to Commander Moshe Mizrahi, the former chief investigator of the Israel police.

"They're going to check who is behind the big money that Talansky raised," he said.

"Talansky acted as fund-raiser, funnelling other people's funds to Olmert. The police need to identify those other donors and find out what interests they represented.

"They will look at why these donors wanted Olmert to intervene for them. We still do not know who they are."

According to Commander Mizrahi, police are already near the stage of being able to recommend that Mr Olmert be indicted for violation of public trust, and could choose to investigate allegations of bribery at a later stage.

Mr Olmert has said he will stand down if he is charged with a criminal offence.