Olmert's office made it clear he did not intend to stand down as caretaker PM
Tzipi Livni, the leader of Israel's ruling party, has called on caretaker Prime Minister Ehud Olmert to quit.
Attorney-General Menachem Mazuz has told Mr Olmert he is considering indicting him on corruption charges.
The prime minister has consistently denied any wrongdoing, but he resigned earlier this year following a number of allegations.
Ms Livni, who is preparing for February general elections, is likely to take over as caretaker PM if he steps down.
On Wednesday, Mr Mazuz said Mr Olmert would be offered a court hearing before he made the final decision on whether to indict him on charges including fraud, false documentation and tax evasion.
"Israel cannot tolerate a situation where he is acting as prime minister after a decision to indict him. This is a moral test, this is a question of values," Ms Livni told a meeting of her Kadima party.
While technically Mr Olmert cannot resign from the post, he could declare himself incapacitated or take extended leave.
Mr Olmert has been repeatedly questioned by the police in a series of investigations into alleged fraud and bribery.
Mr Mazuz said he was considering charging him over allegations that he double-billed government agencies for trips abroad.
He formally resigned in September, but remains as caretaker prime minister. He was succeeded as leader of the ruling Kadima party by Ms Livni, the foreign minister.
Ms Livni announced in October that she had failed to form a coalition. General elections are scheduled for 10 February.
A statement from Mr Olmert's office said he did not intend to leave his position at the head of the caretaker government.
"In these circumstances, there is no legal reason to announce a further resignation," it read.