The Palestinians see the results of Tuesday's election in Israel as a chance to break the stalemate in the peace process with Israel. In a press conference in Ramallah on Thursday, Yasser Abed Rabbo, a senior aide to Palestinian Authority President Mahmoud Abbas, said that Abbas would invite Israeli politicians to a meeting to discuss prospects for future negotiations.

"We invite the Israeli parties, particularly the new ones, for dialogue on future accords," Abed Rabbo said.

He did not say when the invitations would go out, but emphasized that Abbas wanted the meeting to take place before the next Israeli government is formed.

A Palestinian official in Ramallah told Israel Hayom on Thursday that Rabbo's words were directed toward Yair Lapid and members of the Yesh Atid party, which won 19 Knesset seats in Tuesday's election, making it Israel's second-largest party.

Asked whether Lapid would accept the invitation, Lapid's office said: "These are sensitive issues which are not to be dealt with through the media."

Lapid has said he wants Israel to make a serious push for peace, though it is unclear how far he will press the issue in coalition negotiations with Prime Minister Benjamin Netanyahu. In recent public appearances, Lapid has barely breached the issue, focusing instead on domestic economic issues.

Due to its success in the election, Lapid's Yesh Atid party is seen as key to Netanyahu being able to form a stable governing coalition.

Netanyahu and Lapid met on Thursday, but formal coalition negotiations will only start next week.

Lapid campaigned on a domestic agenda that included ending draft exemptions and government stipends for ultra-Orthodox Jews. But two incoming Yesh Atid Knesset members said Thursday that making peace with the Palestinians is just as important to Lapid.

Lapid might be forced to choose between those two issues because it seems nearly impossible to form a coalition that will confront both issues.

Abbas and his advisers were surprised by the strong showing of Israel's center-left parties in the election, after pre-election polls predicted a solid majority for religious and right-wing parties opposed to concessions to the Palestinians.

Instead, the right-wing bloc won a total of 61 seats, compared to 59 for center-left and Arab parties. Netanyahu has said he wants a broad coalition to ensure stability and address domestic issues.

Israeli-Palestinian talks on the terms of Palestinian statehood have been frozen in recent years.

Abbas has argued that he cannot negotiate while Israel continues to build in settlements on lands the Palestinians want for their state. Netanyahu rejects demands for a settlement-construction freeze.

The Palestinians want a state in the West Bank, Gaza Strip and east Jerusalem, territories Israel conquered in the Six-Day War in 1967. Netanyahu has refused to recognize the 1967 borders as the basis for future negotiations.

Since the breakdown of peace talks, Abbas has periodically met with leftist and centrist Israeli politicians, trying to explain his position and counter Israeli allegations that he is not a partner for peace.

Abbas has told them that his U.N. statehood bid was not an attempt to bypass talks, as Netanyahu has claimed, and was meant to increase his leverage in upcoming talks.

Abbas' detractors in Israel argue that he is setting preconditions for negotiations — a claim the Palestinians deny — and that he does not speak for all Palestinians. Gaza is ruled by the Islamic terrorist group Hamas, which violently seized control of the coastal enclave in 2007.

After the Palestinians were granted non-member observer state status by the U.N. General Assembly in November, Abbas formed a committee of Palestine Liberation Organization officials and members of his Fatah movement to do more to reach out to the Israeli public. Many Israelis, even leftists, are skeptical about peace efforts after years of failed negotiations and frequent outbreaks of violence.

Abbas hopes to brief Israeli politicians on his negotiations with Netanyahu's predecessor, Ehud Olmert, in 2008, and to reassure them that he is serious about peace talks, said a member of the committee who spoke on condition of anonymity because he was not authorized to discuss internal deliberations.

Abbas and Olmert made some progress toward a final deal, though gaps remained on key issues. Negotiations broke off in late 2008, as Olmert battled corruption allegations and was eventually forced to resign.

Abed Rabbo said Thursday that the Palestinians have not dropped two longstanding conditions for negotiations — Israel must stop settlement building and the contours of the Palestinian state must be negotiated on the basis of the 1967 borders.

Lapid, meanwhile, has insisted that Israel must retain east Jerusalem, the Palestinians' hoped-for capital, and has not said whether he would push for a settlement freeze to clear the way for negotiations. But the overall tone of his party has been far more conciliatory than Netanyahu's approach in recent years.

Yael German, an incoming legislator in Yesh Atid, said her party is serious about restarting negotiations.

"We will insist on equality of the burden (of military service) but we will also insist on an immediate start to peace negotiations, not just to get into negotiations but in order to reach a final status agreement with the Palestinians," she told Channel 2 on Thursday.

Rabbi Dov Lipman, another Yesh Atid lawmaker, told The Associated Press: "We will not sit in a government that is not moving forward on both issues, and we have no doubt that we can make that happen."

Yisrael Beytenu Chairman Avigdor Lieberman, a key Netanyahu ally who until recently was foreign minister, told Israel Radio that the next government must focus on domestic issues rather than peacemaking to avoid political paralysis, given lawmakers' sharply divergent views.

"If we want to founder from the outset, and embark upon endless internal struggles, then make foreign policy the top priority," he said.