JERUSALEM — Israeli authorities said yesterday that they were opening a criminal investigation into Prime Minister Olmert’s role in the sale of one of Israel’s largest banks, the latest setback for the increasingly unpopular leader.

Mr. Olmert’s public standing has plummeted after last summer’s inconclusive war in Lebanon and a series of corruption scandals involving top officials, but there appeared to be no immediate danger to the stability of his government.

Officials said the investigation would look into the government’s 2005 sale of a controlling interest in Bank Leumi, one of the country’s largest financial institutions.

The state comptroller, a government watchdog, has alleged that Mr. Olmert favored business associates during the sale. Mr. Olmert was finance minister at the time.

The Justice Ministry said a review of the comptroller’s report “led to the conclusion that a foundation of evidence has been built that would justify opening a criminal investigation.”

Police spokesman Micky Rosenfeld said the police anti-fraud unit would handle the probe.

Mr. Olmert, who has been dogged by corruption allegations during his three-decade political career, has denied any wrongdoing in the case. His lawyer, Eli Zohar, said Mr. Olmert looked forward to a chance to clear his name.

“I welcome the decision to open an investigation so that once and for all we can end this irrelevant misunderstanding,” Mr. Zohar told Israel Radio. “We hope the investigation will be conducted quickly and efficiently so that the witch hunt and criticism will disappear.”

If Mr. Olmert were indicted, he would have to step down. But it could be months before a decision is made. Police must complete their investigation, then present their findings to the attorney general’s office, which has the final say on whether to indict.

Attorney General Meni Mazuz has removed himself from the case because his sister holds a senior position at the Finance Ministry and took part in the Bank Leumi privatization process.

While the investigation proceeds, there should be no threat to Mr. Olmert’s coalition government, said Reuven Hazan, a political scientist at Hebrew University in Jerusalem. However, he said it would cause further damage to Mr. Olmert’s already dismal standing with the public.

An opinion poll published last week showed Mr. Olmert’s approval rating at just 14%, and the hard-line Likud Party would win if new elections were held.

“From the eyes of the public at large, this is the continued loss of faith in a leader who seems to be incapable … and unfit to hold power,” Mr. Hazan said. “I’m sorry to say he was already so far down with his approval ratings in the teens or single digits, there’s not much further to fall.”