* U.S.-Israeli rift remains over settlement freeze

* Netanyahu to meet U.S. envoy Mitchell this month

* Barak wants settlement issue put in "proper perspective"

(Adds Abbas quotes paragraphs 11, 12)

By Jeffrey Heller

JERUSALEM, July 1 (Reuters) - Defence Minister Ehud Barak said on Wednesday Israel would consider a limited moratorium on new construction in Jewish settlements, linking the step to U.S. efforts to bring Arab states into a broad peace process.

The offer, which Barak made in a Fox News interview, fell short of Washington's call for a total halt to building in settlements in the occupied West Bank, a demand that has opened the most serious rift U.S.-Israeli relations in a decade.

Barak said a construction freeze was "part of a much wider issue, whether together with the United States and our Palestinian and Arab neighbours, we can launch an original peace initiative to be led by the president of the United States".

Barak held talks in New York on Tuesday with U.S. Middle East envoy George Mitchell in a bid to narrow the division with Washington over the settlement issue.

Palestinian President Mahmoud Abbas has said U.S.-backed peace talks with Israel could not resume until all settlement activity ceased on occupied land Palestinians want for a state.

"Of course there will be a discussion about the contingency that if a major peace initiative is going to be launched, we will probably consider a certain kind of an effective freeze on any new buildings for a limited time period," Barak told Fox.

A joint statement issued after the Barak-Mitchell talks said "steps by Arab states toward normalisation with Israel" and "settlement activity" were among the topics discussed at the meeting.

In an interview with Israel Radio, he said he expected Washington to take a practical approach towards construction work in existing settlements.

Israel hopes to persuade the United States to accept a continuation of existing building projects to meet the needs of the growing population in settlements the Israeli government hopes to keep in any future peace deal with the Palestinians.

"Do you think someone in America thinks that pregnancies can be stopped or that nursery schools shouldn't be built," Barak asked.

In an interview with a Russian channel, Abbas said all Israeli attempts to justify construction at Jewish settlements such as "natural growth" were a "deceit" and will be rejected by major Western powers.

"To be honest, if they would like to continue in this line then they do not want to stop settlement activities. We won't accept, Obama won't accept, Europe and Russia won't accept (any form of continuation of settlement expansion)," Abbas said.

REGIONAL PEACE

Western diplomats said Washington wanted Arab states to let Israel open interest sections and to give Israeli civilian aircraft permission to pass through their airspace.

But the diplomats said Arab states were resisting U.S. pressure, demanding Israel first completely freeze settlement activity and take other steps to bolster the Palestinians.

Barak said the settlement issue, while important, would be "put into the proper perspective" once efforts began to achieve broad Israeli-Arab peace beyond an Israeli-Palestinian deal.

Noting that Israeli Prime Minister Benjamin Netanyahu had pledged not to build new settlements, Barak said the main point of contention with the United States was "what to do with buildings that are now under construction".

Barak said Netanyahu would see Mitchell later this month.

Israeli media reports have said Barak planned to propose a three-month suspension of new construction in settlements, while continuing work on 2,000 buildings currently being erected.

U.S. officials have been cool to a construction freeze that could expire in the middle of peace talks and prompt Arabs to pull out.

Mitchell did not take questions from reporters at the New York hotel where he held talks with Barak. (Additional reporting by Daniel Bases in New York, Adam Entous in Jerusalem and Mohammed Assadi in Ramallah; editing by Tim Pearce)

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