Micha Lindenstrous, Israel's comptroller, has issued a critical report about alleged irregularities in appointments at the ministry of trade and industry, while Olmert was in charge before becoming prime minister earlier this year.
The attorney general must first endorse the recommendation for a police investigation to be opened.
Olmert has been dogged by corruption charges throughout his career but has never been convicted. He has denied any wrongdoing.
Olmert began a battle for his political survival at home after aknowledging shortcomings in the conduct of the month-long war with Hezbollah that ended over two weeks ago.
Opinion polls show public support for Olmert eroding. Critics say the career politician lacks the combat credentials of many of his predecessors.
He has faced a backlash over his decision to accept the UN resolution and for failing to deliver a fatal blow to Hezbollah.
"The overall responsibility for this operation lays with me, the prime minister. I am not asking to share this with anyone"
Israeli prime minister
Army officers said that they were held back during the war and right-wing rivals started calling for new elections in late August.
The next national ballot is not due until 2010.
Hours after Amir Peretz, the Israeli defence minister, called for an investigation into how the war was conducted in mid-August, Olmert said: "There were ... shortcomings. We will have to examine ourselves at all levels.
"The overall responsibility for this operation lays with me, the prime minister. I am not asking to share this with anyone."
After weeks of political wrangling, all parties agreed that an investigatory commission be set up to look into how the war was conducted. The commission will be headed by Nahum Admoni, who was head of Israel's Mossad intelligence agency during the 1980s.
Olmert said the commission will be charged with "examining the performance of the government, its proceedings and decision-making and anything else it sees fit. The government will not be exempt from professional examination and criticism".
Olmert said that a second panel, headed by Israel's state comptroller, will look at management of the civilian side of the war, such as delivering aid to northern towns hit by Hezbollah rockets.
The committees will work alongside a third investigation, appointed by Peretz, to look into the military's handling of the war. That committee, headed by a former army chief and comprised of ex-military men, has been criticised as toothless.
"The government will not be exempt from professional examination and criticism"
Israeli prime minister
It suspended work after just one meeting, waiting for guidance from Olmert.
Critics have been demanding a full-blown state inquiry, with the authority to fire officials. Israel has carried out such inquiries in the past, including after the 1982 war in Lebanon. That probe led to the dismissal of then-defence minister Ariel Sharon.