President Mahmoud Abbas’ main target appears to be Yair Lapid, leader of the moderate Yesh Atid (There is a Future) party, who is expected to be influential in setting the priorities of the next government.

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, he has barely breached the issue, focusing instead on domestic economic concerns.

In elections this week, Lapid’s party emerged as the second largest with 19 of 120 seats in parliament, after Netanyahu’s right-wing Likud-Yisrael Beitenu bloc that won 31 seats. Netanyahu will keep his job, but will have to bring other parties into his government to win a parliamentary majority, and Lapid’s faction is seen as key to any stable coalition.

Netanyahu and Lapid met Thursday, two days after the election, though formal coalition negotiations will only start next week, and could take up to six weeks.

Lapid has campaigned on a domestic agenda that includes ending draft exemptions and government stipends for ultra-Orthodox Jews. But two incoming legislators from his party said Thursday that making peace with the Palestinians is just as important to him.

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

Netanyahu is a hardliner and may balk at excluding right-wing parties from his coalition in order to move forward with peace talks.

At the same time, efforts to draft Jewish seminary students would likely invite the pro-settler Jewish Home party into the government. The party looks willing to cooperate on that front but wants to annex some of the lands the Palestinians want for their state.

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

Instead, hawkish and religious parties won a total of 61 seats, compared to 59 for center-left and Arab parties. But Netanyahu has said he wants a broad majority to ensure stability and address domestic issues.

Hoping to capitalize on the results, Abbas will invite representatives of Israeli parliament factions to discuss prospects for negotiations, Abbas aide Yasser Abed-Rabbo said.

“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 Israel forms its next government.

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.”

Israeli-Palestinian talks on the terms of Palestinian statehood have been frozen since Netanyahu took office four years ago.

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

The Palestinians want a state in the West Bank, Gaza and east Jerusalem, territories Israel captured in 1967, but Netanyahu refuses to recognize the 1967 lines as a base for future border talks.

Late last year, the U.N. General Assembly recognized a Palestinian state in the territories captured in 1967, boosting the Palestinian position on borders.

Since the breakdown of talks, Abbas has periodically met with dovish 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. 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 does not speak for all Palestinians. Gaza is ruled by the Islamic militant Hamas, which seized the territory in 2007.

In the wake of the U.N. recognition, Abbas formed a committee of PLO officials and members of his Fatah movement to do more to reach out to the Israeli public. Many Israelis, even dovish leftists, have expressed skepticism over peace efforts after years of failed negotiations and frequent outbreaks of violence.

In the planned meetings with Israeli politicians, Abbas hopes to brief them on his negotiations with Netanyahu’s predecessor, Ehud Olmert, in 2008, and 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 borders Israel held before 1967.

Lapid, meanwhile, insists 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 Israel TV’s 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.”

Avigdor Lieberman, a key Netanyahu ally who until recently was foreign minister, told Israel Radio 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.