The Palestinian president said talks with Ehud Olmert, Israel's acting prime minister, should be held as soon as possible.
"I am ready to meet him as soon as possible and I hope to sit round the negotiating table immediately," Abbas said in Ram Allah on Wednesday.
"The only way we can forge peace is through negotiations and not through killings, assassinations, attacks and unilateral measures."
However, Hamas, which has spearheaded the resistance against Israel in recent years, is expected to make a strong challenge to Abbas' ruling Fatah party and earn a place in the next government.
A coalition government involving Hamas could make it difficult for Israel and the Palestinians to restart long-frozen peace efforts.
"If I feel that I can't fulfil this programme ... then the seat is not my ultimate ambition," Abbas said, referring to his post as Palestinian president.
Abbas's comments came after Olmert said on Tuesday he hoped to resume negotiations with the Palestinian leadership after Israel's general election on 28 March.
Ariel Sharon, the prime minister of Israel, who has been in a coma since suffering a brain haemorrhage two weeks ago, and Abbas met twice last year.
"The only way that we can forge peace is through negotiations and not through killings, assassinations, attacks and unilateral measures"
However, since a heated summit in June, the Israeli leader had declined to meet the Palestinian Authority president.
Sharon boycotted Yasser Arafat, Abbas's predecessor who died in November 2004, and also withdrew troops and settlers from the Gaza Strip last summer on a unilateral basis.
Olmert has said there could be no progress on the peace process if Hamas, the Islamist resistance group, entered a Palestinian government after elections in the West Bank and Gaza next Wednesday.
Meanwhile, Israeli police detained seven Palestinian activists campaigning in Arab East Jerusalem for next week's parliamentary election, accusing them of belonging to an outlawed group.
Shmuel Ben-Ruby, a spokesman for Jerusalem police, said the activists were taken for questioning while they were trying to convene a news conference at a hotel.
Among those in custody was the Jerusalem head of the Popular Front for the Liberation of Palestine, a group outlawed by Israel for involvement in attacks against its civilians during a more than five-year Palestinian uprising, police said.
Israel recently lifted a ban on
voting in East Jerusalem
Police have previously arrested several members of Hamas for campaigning in Jerusalem, a city Israel regards as its capital, but which Palestinians also see as theirs.
Mickey Rosenfeld, a spokesman for national police, said other groups outlawed by Israel, such as the Popular Front, would also be stopped from campaigning in East Jerusalem.
It appeared to be the largest number of Palestinians held in the city for campaigning since the Israeli government agreed on Sunday to approve voting on 25 January in East Jerusalem.
Meanwhile, Abbas reiterated his demand that armed Palestinian groups give up their weapons and submit to the security forces, a demand that has been uniformly ignored in chaotic Palestinian areas. Abbas said the 11 parties participating in the election had a responsibility to disarm.
"It is not their right to participate in political life and maintain militias," he said. "There should be no one armed beyond the law."
Abbas promised that the elections would be clean and honest and warned gunmen not to bring arms to polling stations.