RAMALLAH, West Bank – The Palestinians are ready to ease their demand for a freeze on Israeli settlement construction to get peace talks back on track, a top official told The Associated Press on Thursday.

The softened position reflects the Palestinians’ growing realization that their alternative strategies to talks — reconciling with the Hamas militant group and seeking unilateral recognition at the United Nations — are both in trouble.

The official, who spoke on condition of anonymity, said the Palestinians will ease the demand for a full construction freeze and resume peace talks if Israel accepts President Obama’s proposal to base negotiations on a broad Israeli withdrawal from lands captured in the 1967 Mideast war.

The issue is at the heart of the current impasse. The latest round of talks was launched last September at the White House after a two-year breakdown, only to collapse three weeks later with the expiration of an Israeli slowdown on settlement construction.

The Palestinians have been demanding a full freeze on all construction — which would go further than that slowdown — before resuming negotiations. Any move to drop or significantly ease that demand could put greater pressure on Israel to respond positively — perhaps by accepting Obama’s formula, which it has not done.

Officials in the office of Israeli Prime Minister Benjamin Netanyahu wouldn’t comment on the Palestinians’ latest offer.

A new complication emerged earlier this year when Palestinian President Mahmoud Abbas’ Fatah party began unity talks with its rival, Hamas. Israel has said it cannot negotiate with Abbas if he presides over a government that includes the Islamic militant group, which is sworn to Israel’s destruction.

Difficulties that have emerged in implementing the unity pact — especially over the choice of prime minister — could render those objections moot.

With both the reconciliation effort and their U.N. strategy on the rocks, the Palestinians appear to be seeking a face-saving formula that would allow them to restart negotiations.

For months, the Palestinians have been saying there is no point in negotiating if Israel continues to build up Jewish enclaves in the West Bank and east Jerusalem, areas captured in the 1967 Mideast war and claimed by the Palestinians for their future state.

But on Thursday, the senior Palestinian official told the AP that the Palestinians could live with a construction slowdown, in which Israel continues building projects already under construction but agrees not to approve any new projects.

In return, he said the Palestinians want Israel to accept Obama’s plan calling for an independent state based on Israel’s pre-1967 lines, albeit with some modifications through mutually agreed “land swaps.”

The Palestinians have presented their ideas to American mediators visiting the region in recent days in an effort to get long-stalled negotiations moving again, the official said.

An Israeli official, also speaking on condition of anonymity, said Israel was sticking to its line on Hamas, and refused to comment on the settlement issue.