* PLO and Hamas pursue reconciliation talks in Gaza
* Israeli-Palestinian diplomacy faces April 29 deadline
* Netanyahu says Abbas demanding unacceptable conditions (Adds Israeli foreign minister's and Abbas spokesman's comments)
By Jeffrey Heller
JERUSALEM, April 23 (Reuters) - Israel's Prime Minister Benjamin Netanyahu cautioned Palestinian President Mahmoud Abbas on Wednesday over just-revived unity talks with Hamas, saying he had to choose between peace with Israel or its Islamist enemy.
Amplifying Netanyahu's warning, Israeli Foreign Minister Avigdor Lieberman said Abbas's signature on a unity accord with Hamas would be tantamount to "signing the termination of negotiations between Israel and the Palestinian Authority".
Delegates from Hamas and Abbas's Fatah party-led Palestine Liberation Organisation held a fence-mending session on Tuesday in the Gaza Strip, their first since a 2007 conflict in which forces loyal to the Western-backed leader lost control of the enclave to the militant group, an opponent of peace with Israel.
A Palestinian official who attended Tuesday's meeting said there had been an "agreement in principle" on forming a "government of experts" - or a cabinet staffed by technocrats rather than politicians, possibly within five weeks. A PLO-Hamas news conference was expected later on Wednesday.
But Palestinian hopes of reconciliation have been dashed repeatedly in the past. Since 2011, Hamas and Fatah have failed to implement an Egyptian-brokered unity deal because of disputes over power-sharing and the handling of the conflict with Israel.
The new bid for reconciliation coincided with meetings between Palestinian and Israeli negotiators to try to extend U.S.-sponsored peace talks beyond an April 29 deadline. Sources from both sides said strong disagreements remained after they convened in Jerusalem on Tuesday.
Netanyahu, in remarks to reporters as reports of a possible unity deal emerged, asked: "Does he (Abbas) want peace with Hamas or peace with Israel?"
"You can have one but not the other. I hope he chooses peace. So far he hasn't done so," he said.
Abbas's spokesman, Nabil Abu Rdeineh, said Palestinian unity was an internal matter.
"Abbas chooses peace and the unity of the Palestinian people," Abu Rdeineh said. "The choice of unifying the Palestinian people enforces peace, and there is no contradiction whatsoever between reconciliation and negotiations."
Lieberman, in a statement released by his spokesman, said Abbas, who heads the Palestinian Authority that exercises limited self-rule in the occupied West Bank, "cannot make peace both with Israel and Hamas, a terrorist organisation that calls for Israel's destruction".
TROUBLED PEACE TALKS
An agreement, paving the way for elections and a national strategy towards Israel, could not only give Abbas a measure of sovereignty in Gaza but also help Hamas, hemmed in by an Israeli-Egyptian blockade, become less isolated.
In the troubled Israeli-Palestinian negotiations, both sides have said they are willing to extend the talks championed by U.S. Secretary of State John Kerry.
However, Netanyahu accused Abbas on Wednesday of making unacceptable demands. Meeting Israeli journalists on Tuesday, Abbas had said Israel should commit to freezing settlement activity on occupied land and focus on demarcating the borders of a future Palestine.
"We're trying to re-launch the negotiations with the Palestinians," Netanyahu said. "Every time we get to that point (Abbas) stacks on additional conditions which he knows that Israel cannot give."
Abbas told the reporters that Israel, as the occupying power in the West Bank, would be obliged to take on the administrative and financial burden of governing Palestinian areas.
Kerry revived the peace talks in July after a nearly three-year hiatus, with the aim of ending a decades-old conflict and establishing a Palestinian state in the West Bank and Gaza Strip, with East Jerusalem as its capital, alongside Israel.
The negotiations plunged into crisis this month when Israel refused to carry out the last of four waves of prisoner releases unless it received assurances the Palestinian leadership would continue the talks beyond the end of April.
After Israel failed to free the prisoners, Abbas responded by signing 15 international treaties, including the Geneva Conventions on the conduct of war and occupations. Israel condemned the move as a unilateral step toward statehood. (Additional reporting by Nidal al-Mughrabi in Gaza and Ali Sawafta in Ramallah; Editing by Louise Ireland)