JERUSALEM - Police questioned Prime Minister Ehud Olmert for four hours Thursday, his second interrogation this week over allegations that he interfered in the sale of Israel's second largest bank to help his friends.

The investigation into the privatization of Bank Leumi is one of two criminal probes facing Olmert. He also is suspected of buying a Jerusalem home from a real estate developer at a substantial discount in return for helping the builder obtain construction permits from Jerusalem authorities.

Police questioned Olmert at his official residence in Jerusalem, looking into a possible breach of trust, police spokesman Micky Rosenfeld said. Olmert was questioned for five hours Tuesday. There is no date for further questioning, and the evidence gathered will be passed on to the state attorney's office, Rosenfeld said.

He gave no other details, citing the sensitivity of the issue. If indicted, Olmert would have to step down, but that stage would be at least several months away.

Olmert has denied any wrongdoing. But the investigations have embarrassed the prime minister just as his popularity is starting to rebound from harsh criticism for his handling of last year's inconclusive war in Lebanon.

Police suspect Olmert tried to rig the sale of Bank Leumi in favor of two associates when he was finance minister in 2005. The associates, Australian real estate developer Frank Lowy and American billionaire S. Daniel Abraham, never submitted a formal bid for the bank.

Olmert has said he is confident he will be cleared. His office declined to comment on the investigation, but expressed confidence before questioning began Tuesday.

"At the end of investigation, it will emerge that all the decisions taken with regard to the privatization of Bank Leumi were professional and taken judiciously following consultations with relevant sources, and that his actions were above reproach," his office said.

Olmert has faced repeated allegations of corruption throughout his three-decade political career, but he has always proclaimed his innocence and has never been convicted.

In a separate investigation, police questioned a lawmaker for two hours Thursday on suspicions of sexual harassment. Police are looking into allegations that Izhak Ziv, of the Pensioners Party, harassed a female party activist.

Rosenfeld said Ziv would be questioned further, but had no information when that would happen. He also gave no details on the alleged incident involving Ziv and the woman.

But the Israeli paper Yediot Ahronot reported that Ziv, 69, allegedly fondled the woman in a bedroom at his home before the 2006 parliamentary elections.

The paper reported the woman tried to resist, but Ziv threw her down on the bed. She then managed to get away and flee the apartment, it reported.

Ziv's office could not immediately be reached for comment.

Israeli media reports have quoted Ziv's aides as saying the sexual harassment charges are part of a long-standing political feud between the lawmaker and the woman.