FACTBOX: Investigations affecting Israel PM Olmert

(Reuters) - A police investigation covered by a sweeping media gag order has sparked intense speculation that Israeli Prime Minister Ehud Olmert might be forced to resign.

He has weathered previous investigations, as follows:

* In March 2006, Israel's state comptroller cleared Olmert of any wrongdoing in the sale of a Jerusalem apartment. At the same time the comptroller queried Olmert's 2005 purchase of an apartment in Tel Aviv. That case was closed earlier this year.

* In January 2007, prosecutors investigated allegations that Olmert, when finance minister, had tailored a 2005 tender for the sale of state-owned Bank Leumi to favor an investment firm partly owned by a friend. The case was dropped in November.

* In September 2007, attorney-general ordered police to open a criminal investigation into Olmert's purchase of a home in Jerusalem. Olmert, who was mayor of Jerusalem for 10 years until 2003, denies any wrongdoing in response to allegations that his purchase in 2004 was a bargain granted in return for favors.

* In October last year, police launched an investigation into Olmert's conduct as industry, trade and labor minister in 2003. He denies any wrongdoing in response to allegations he may have favored personal associates for positions and funding.

* On May 2, Olmert was questioned by police at short notice. He later condemned "malicious rumors" circulating around the matter and allies have accused right-wingers of trying to undermine Olmert's U.S.-sponsored peace talks with the Palestinians. A sweeping gag order bars reporting on the case.

* Aside from legal investigations, Olmert's tenure has been marked by an official inquiry into his conduct of the 2006 war against Lebanese Hezbollah guerrillas. Despite the Winograd Commission's preliminary criticism in April 2007 and its final conclusion in January that there were "serious failings" by Israeli leaders in the war, Olmert resisted calls to resign.