"When a new [Kadima party] chairman is chosen, I will resign as prime minister to permit them to put together a new government swiftly and effectively."
Al Jazeera's Jacky Rowland, reporting from Jerusalem, said that very few observers believed that Olmert would go through the "humiliating" process of applying for his own job.
"The only reason Kadima is actually holding primaries is because Ehud Olmert is now seen as a political liability," she said.
"No surprise then that he is not standing in the leadership primary, but clearly he decided to move quickly to remove any remaining doubt, and so the party can move towards a leadership election without Olmert hanging around the party like a millstone around its neck."
Olmert said he was "sorry" for any mistakes he may have made, but his brief address included harsh criticism of the police investigation into the corruption allegations against him.
"I was forced to defend myself against relentless attacks from self-appointed 'fighters for justice' who sought to depose me from my position," he said.
"I will quit my duties in an honourable, just and responsible manner, as I have acted throughout my mandate," Olmert said. "I will then prove my innocence."
Moshe Lador, the state prosecutor, said last week that he would decide whether to indict Olmert over one of the corruption cases "very soon".
|Livni, left, is seen as the frontrunner to replace Olmert in Kadima [AFP]
Morris Talansky, the US businessman at the centre of the allegations, said in testimony to prosecutors in May that he had given money to Olmert on multiple occasions to cover expenses for his stays in the US and pay for his election campaigns as Jerusalem mayor and a Likud MP.
David Chater, reporting from Jerusalem for Al Jazeera, said all eyes are focused on the ruling Kadima party's primaries in September.
Tzipi LIvni, the Israeli foreign minister, is the main contender and holds a "narrow lead" inside the party, said Chater.
But he added that Shaul Mofaz, the transport minister, was closing the gap and that the former chief of the Israeli army is thought by political insiders to have the "right stuff" to lead the party and the country.
Olmert's successor as Kadima party leader would not automatically take over as Israel's prime minister.
He or she would first have to forge a coalition government, a challenge that could prove time-consuming and complicated because of bitter divisions within parliament.
Olmert's announcement came while Livni was in the US for talks on the Middle East peace process.
While it was not immediately clear what Olmert's decision to step down would have on the talks, Ahmed Qureia, the chief Palestinian negotiator and former prime minister, said Olmert's departure would not affect negotiations.
"Since we want peace and want to negotiate with the Israeli government, we are not dealing with individuals, but the government as a whole.
"Whether he [Olmert] is still the prime minister for two days or two months, we will continue to deal with him. If someone comes, we will deal with them, as long as they want to deal with us."
Al Jazeera's Rowland said that the talks with the Palestinians, as well as the indirect negotiations with Syria being mediated by Turkey, were "much bigger than the individual man of Ehud Olmert".
"But obviously in terms of seeing Olmert himself do anything dynamic or far reaching in terms of the international scene the clock is now ticking."
The Israeli prime minister suggested earlier this week that there was little chance of reaching the end of the year deadline as it would be impossible to agree on the crucial issue of Jerusalem.
Washington responded to Olmert's announcement by saying it was prepared to work with any Israeli leader.
"We are going to look forward to working with all responsible Israeli leaders in the government, whether it is this government or future governments," Sean McCormack, US state department spokesman, said.
Sami Abu Zuhri, a senior Hamas official, called Olmert's announcement "a victory" for the group, which has controlled the Gaza Strip since it pushed out security forces loyal to Mahmoud Abbas, the Palestinian president.