Foreign Affairs Minister John Baird is gauging the dynamics of the new Israeli government, trying to determine how the motley combination of coalition partners will affect potential talks with Palestinians.

Prime Minister Benjamin Netanyahu's new coalition is a hodgepodge of parties with clashing views on striking a peace deal.

On Monday, Mr. Baird met with Naftali Bennett, the Minister of Economy and Trade in the new coalition. Mr. Bennett is the leader of the right-wing Jewish Home party, which opposes the establishment of a Palestinian state.

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On Tuesday, Mr. Baird will meet with other key players in the coalition, including Finance Minister Yair Lapid and Justice Minister Tzipi Livni, whose parties favour peace talks; Avigdor Lieberman, the former foreign affairs minister who merged his right-wing party with Mr. Netanyahu's Likud; and Mr. Netanyahu himself.

On a day when U.S. Secretary of State John Kerry was in Israel to push for a revival of moribund peace talks, the mishmash of parties in Israel's governing coalition leaves open the question of whether Mr. Netanyahu can find a negotiating position that his coalition will support.

Mr. Baird asked that very question in his meeting with Mr. Bennett, according to aides, inquiring how he works in cabinet with a figure like Ms. Livni, a prominent supporter of a two-state solution who is mandated as the new government's peace negotiator.

The Foreign Affairs Minister emerged expressing surprise at the left-right combination in Mr. Bennett's policies. Mr. Baird told the meeting that he favours measures to improve the day-to-day lives of Palestinians like reducing waits at security checkpoints between the Palestinian Authority's territory in West Bank and Israeli-controlled territory. Later, as he chatted with an Israeli TV interviewer, he said he tried not to prejudge Mr. Bennett. "I don't agree with all of his policies, but he was very reasonable," he said.

Mr. Kerry is said to be seeking to revive peace talks based on a modified version of the 2002 Arab peace plan, which called for guarantees of peace from other Mideast nations and separate Israeli and Palestinian states.

In an interview with The Globe and Mail, Palestinian Authority President Mahmoud Abbas warned that time is running out for a two-state solution – and the current push may be the "last opportunity." He confirmed he wants Mr. Kerry to convince Mr. Netanyahu to put his own proposals for borders on the table, but Israeli officials rejected that call.

Mr. Abbas has long insisted that Israel must stop all settlement activity before talks begin. Mr. Baird, when asked about settlements in his interview with Israel's Channel 10, called them "distinctly unhelpful" but repeated his call for talks to begin without preconditions.

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"We think unilateral actions on either side, on behalf of the government of Israel or the Palestinian Authority, are distinctly unhelpful in the search for peace," he said. "But one of the things that we strongly believe in is that the parties have got to stop negotiating about the negotiations and sit down and begin to talk peace."

Editor's Note: An earlier version of this story referred to Yair Lapid as a former finance minister. He is Israel's current finance minister. This version has been corrected.