Olmert, weakened by Israel's war in Lebanon and forced to shelve promises to withdraw from the occupied West Bank, also said he would meet the US president in November, in part to turn the screws on arch-enemy Iran.
But his invitation to Siniora was swiftly rebuffed.
"I am ready to meet with him (Abbas) immediately if he wants to talk about the roadmap," Olmert told the Knesset at the opening of its winter session, reiterating frequent calls in recent weeks to meet the Palestinian leader.
The roadmap has stalled ever since its 2003 launch. Drafted by the European Union, Russia, United Nations and United States, the blueprint envisions an independent Palestinian state living side by side in peace with Israel.
Abbas, who has proved unable to persuade ruling Islamist movement Hamas to accept international demands to recognise Israel, has repeatedly said he is willing to meet Olmert provided such talks are well-prepared in order to achieve results.
Only on Sunday, however, Olmert said efforts to set up a meeting with Abbas, whom he last met informally in June, were at a dead end because the Palestinian president conditioned such talks on the release of prisoners.
Olmert drew a distinction between Abbas and Hamas, which Israel and the West boycott as a terrorist organisation, saying his willingness to meet the president did not mean the Jewish state was softening toward the Islamists.
"As long as Hamas does not recognise Israel, past agreements and does not act to end terrorism, we will not engage with it in dialogue. We will not renounce these conditions," Olmert told parliament.
Setting his sights on Lebanon, he urged Siniora to meet for peace talks following this summer's devastating 34-day war against Hizbullah, in what would be the first such summit.
"I call on Lebanese Prime Minister Fuad Siniora to meet with me to establish peace between us and Lebanon," he said.
The two countries have not had official relations since the establishment of the Jewish state in 1948.
But the Lebanese leader quickly rejected Olmert's call, albeit implicitly, by reiterating that Beirut would be the last Arab country to sign a peace deal with Israel.
"Real peace resides in Israel accepting the Arab peace initiative, promoted at the time by prince (now King) Abdullah of Saudi Arabia and agreed to at the Arab League summit held in Beirut," Siniora's office said.
Fixing his attention on chief ally the United States and Iran, Olmert told MPs he would meet US President George W. Bush in November, without setting a specific date, in part to discuss Tehran's disputed nuclear program.
"The Iranian nuclear menace is an existential menace for Israel, for world peace," Olmert declared on the eve of leaving for a three-day visit to Moscow for talks with Russian President Vladimir Putin.
A government official told AFP that Olmert will be travelling to the United States on November 13 for meetings with Bush and administration officials.

Copyright AFP (Agence France-Presse), 2006