Israeli right-wing opposition leader Binyamin Netanyahu has called for snap elections, after Prime Minister Ehud Olmert announced he would stand down.
Mr Netanyahu said the government had "finished its mission" and was responsible for a "string of failures".
Mr Olmert announced on Wednesday that he would not stand in a leadership race for his Kadima Party set for September.
He was under increasing pressure to quit over mounting corruption allegations, which he denies.
Allies and opponents of Mr Olmert alike have backed his decision to quit.
He plans to remain as caretaker PM until a new government is formed.
'Correct decision'
Ex-PM and Likud Party leader Mr Netanyahu told public radio on Thursday: "This government has finished its mission, irrespective of who will head Kadima.
"Everyone in this government is responsible for a string of failures. We must let the people decide through new elections."
The BBC's Wyre Davies in Jerusalem says there are fears that unless a successor can quickly form a new government, Mr Olmert may limp on as a caretaker leader for several weeks.
He says many observers believe that scenario is unlikely to help Israel and the Palestinians reach a deal by the end of the year, the aim under the current US-backed peace process.
Mr Olmert's main coalition partner, the Labour Party leader and Defence Minister Ehud Barak, said he believed Kadima could form a new government without a new general election.
An opinion poll released just before Mr Olmert's announcement suggested Israeli voters thought Mr Netanyahu would make the best premier, ahead of Foreign Minister Tzipi Livni.
Ms Livni, a favourite to replace Mr Olmert as head of the Kadima Party, said the prime minister's decision had been hard but correct.
A former protege of Ariel Sharon, she helped broker Israel's withdrawal from the Gaza Strip and has championed a vision of Israel co-existing with a Palestinian state, say analysts.
But critics argue she lacks the military and political experience to lead the country.
Transport Minister Shaul Mofaz, another main contender to replace Mr Olmert, has said that if he wins the party contest, he is confident of winning enough support to form a workable coalition government.
More politically experienced than Ms Livni and with a strong background in the military, he could prove more appealing to smaller right-wing and religious parties, according to our correspondent.
Public Security Minister Avi Dichter and Interior Minister Meir Sheetrit are also seen as potential successors.
Mr Olmert faces a corruption inquiry over allegations that he received illegal campaign donations from businessman, Morris Talansky, and that some of the money was used to buy luxury items.
He has not been charged, and denies the allegations.
The scandal is one of six corruption investigations Mr Olmert has faced during his time in office.
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