|Mofaz, left, and Livni, centre, will compete to succeed Olmert [EPA]
Israel's ruling Kadima party will hold primaries on September 17 during which registered members will choose a successor to Ehud Olmert as the party chairman.
At least three Kadima ministers are expected to take part in that election.
Tzipi Livni - The foreign minister and chief negotiator with the Palestinians has been called the most powerful woman in Israel since Golda Meir, the prime minister in the 1970s.
Last year she called on Olmert to quit after the prime minister was criticised in a report on the conduct of Israel's war against Hezbollah in Lebanon.
Livni is a former intelligence agent and like Olmert and Ariel Sharon, the former prime minister, she left the Likud party to form Kadima in 2005.
Shaul Mofaz - A deputy prime minister and the current minister of transport is probably more notabe as a military man.
He joined the Israeli army after leaving high school, eventually rising to chief of staff. Later he was named defence minister.
Mofaz is well-known for his tough tactics in crushing a Palestinian uprising after peace talks failed in 2000 and has already launched his own campaign for the Kadima leadership.
Avi Dichter - The minister for public security was a member of an elite army unit and the Shin Bet intelligence agency before joining Kadima in 2005.
He gained a seat in the Knesset in March 2006 and he has expressed doubts about the current peace process with the Palestinians.
If Olmert's successor is able to form a coalition government it would take office once sworn in by parliament in late October. Olmert would remain caretaker prime minister until then.
However, some of Olmert's coalition partners may not want to link up with Livni, who is seen as being somewhat moderate politically.
These parties could throw their weight behind Benjamin Netanyahu, the parliamentary opposition leader and chairman of the Likud party, encouraging Shimon Peres, the president, to ask him to try to form a government.
If no coalition can be formed, or a majority in parliament votes to dissolve itself, an election would have to be held, bringing forward polls not scheduled to take place until 2010.
An election must be held within five months of the Knesset voting to dissolve itself - the gap is usually shorter in practice - leaving Olmert as caretaker prime minister for several more months.
Recent opinion polls suggest that Netanyahu's Likud party would win a snap election, positioning him as favourite to become the new prime minister, however others outside Kadima could also be in the frame.
Benjamin Netanyahu - The prime minister from 1996 to 1999 and leader of Likud party since Sharon, Olmert and Livni, among others, formed Kadima.
Educated in the US, he became a decorated commando before entering politics.
As finance minister under Sharon from 2003, Netanyahu, pushed through economic changes that angered the left but are credited by some with boosting economic growth.
Ehud Barak - Another former prime minister and highy decorated commando, Barak is now the defence minister and leader of the Labour party, Kadima's main coalition ally.
When he campaigned for the Labour leadership last year, he said Olmert should quit if the report in to the war with Hezbollah criticised him. It did, but Barak said he would wait and urge Olmert to go "at a more convenient time".
Barak would have to be elected to the Knesset before he could become prime minister.
Source: Al Jazeera and agencies