By Ori Lewis

JERUSALEM, Jan 15 (Reuters) - Israeli Prime Minister Ehud Olmert will try on Tuesday to keep his coalition government intact by hoping to persuade an important right-wing party not to quit over peace talks with the Palestinians.

Olmert is set to meet Minister for Strategic Affairs Avigdor Lieberman of the Yisrael Beiteinu party later on Tuesday, but his hopes of keeping the 11-seat party in his coalition, which currently numbers 78 members, appear slim.

An official at Olmert's office confirmed the meeting would take place, but did not give a time.

Lieberman has threatened to quit the coalition once talks with the Palestinians moved to discussing "core issues" including borders and the fate of Jerusalem and Palestinian refugees, which must be resolved to end decades of conflict.

Israel and the Palestinians opened their most serious peace talks in seven years on Monday, urged by U.S. President George W. Bush to reach a deal within a year, but domestic troubles have weakened both partners in their home constituencies.

As well as the threat to the integrity of his coalition government, Olmert is likely to face new calls to resign after an inquiry into the 2006 Lebanon war issues its final report on Jan. 30.

Palestinian President Mahmoud Abbas wields little power beyond the West Bank after Hamas Islamists seized control of the Gaza Strip in June.

Ha'aretz newspaper said on Tuesday that Olmert would continue to promote the peace push "even if we have to pay a political price."

Moldovan-born Lieberman, whose party appeals to many voters in Israel's large immigrant community from Russia and other former Soviet states, is expected to announce his decision whether to quit on Wednesday.

Many Israeli pundits suggest that he will leave Olmert's coalition, although they speculate that Yisrael Beiteinu could be substituted by the left-wing Meretz party which has long been an advocate of peace talks with the Palestinians.

The imposing, bearded Lieberman said discussing core issues would be "crossing a red line".

Israeli Foreign Minister Tzipi Livni told parliament on Monday that she would keep details of her talks with former Palestinian Prime Minister Ahmed Qurie confidential, but later told parliament she was "prepared to make significant territorial concessions" to further Israel's interests.

After the talks opened in Jerusalem on Monday, Qurie said that core issues had indeed been discussed.

"We started today talking about all the core issues, Jerusalem, refugees, borders, settlements. We talked about these issues in general. The talks were positive but the path ahead is difficult," Qurie said.

Israeli officials said Olmert was seeking a deal that would outline a "framework" for a Palestinian state with implementation delayed until the Palestinians can ensure Israel's security.

Abbas wants a final peace treaty enabling him to declare a state by the end of the year. (Editing by Dominic Evans)

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