Mr Olmert has insisted he has not done anything wrong

The move came after a government watchdog concluded Mr Olmert paid $325,000 (�162,500) below market value for the house.

The prime minister has protested his innocence, insisting the price was fair and the inquiry was "uncalled for".

But he promised to co-operate fully with the investigators.

The BBC's Raffi Berg in Jerusalem says the police investigation into Mr Olmert's property deal could take several months.

If they eventually recommend charging Mr Olmert, the matter will then go to the state attorney for a final decision, at which point Mr Olmert's job could be on the line, our correspondent says.

'Honest and ethical'

"We are sure the investigation will clearly show that the purchase of the apartment by the Olmert family was made honestly, ethically and for an appropriate price," Mr Olmert's office said in a statement.

OLMERT TIMELINE 1945: Born in Binyamina 1973: Elected to the Knesset 1993-2003: Jerusalem mayor 2003-2006: Ministerial posts April 2006: Prime minister Profile: Ehud Olmert Israel's graft 'epidemic'

Attorney General Menahem Mazuz confirmed that police would investigate what he termed the "Cremieux Street affair", referring to the address of the house bought by Mr Olmert.

Mr Olmert is already being investigated over separate allegations relating to the sale of Leumi bank in 2005.

Several senior officials were arrested as part of a police investigation into possible bribery over the sale.

Other politicians have also been blighted by serious allegations - earlier this year ex-President Moshe Katsav struck a plea bargain with the attorney general to avoid rape charges.

Under the plea, he is due to be charged with lesser sexual offences and faces a suspended sentence.