NEW YORK, Sept 20 (Andrew Quinn/Reuters) - The Quartet of Middle East peace mediators will on Tuesday call on Israel to extend its settlement moratorium, saying the freeze has had a positive impact as the two sides seek a peace deal within the next year, according to a draft statement seen by Reuters.

The Quartet noted that the commendable Israeli settlement moratorium instituted last November has had a positive impact and urged its continuation, said the statement, due to be issued by the Quartet, comprised of the United States, the European Union, the United Nations and Russia.

The Quartet statement, to be issued after a meeting on the sidelines of the U.N. General Assembly, increases pressure on Israeli Prime Minister Benjamin Netanyahu to extend a 10-month settlement freeze due to expire at the end of September.

U.S. President Barack Obama and Secretary of State Hillary Clinton have already urged Netanyahu to extend the moratorium on new settlement activity on land in the West Bank captured in the 1967 war.

The Palestinians have said they will drop out of the peace talks, launched just this month with Obama's backing, unless the freeze continues. But Netanyahu has been reluctant to take that step, which could effect his ruling coalition dominated by pro-settler parties.

The Quartet draft statement repeated the group's backing for the current peace talks and reaffirmed its hopes for a deal within one year that will see a viable Palestinian state emerge side-by-side with Israel.

The statement urged both sides to refrain from provocative actions and inflammatory rhetoric, and called upon Israel to further ease restrictions on Palestinians in the West Bank and Gaza Strip -- a step the World Bank says will be important for the economic viability of a future Palestinian state.

It stressed the importance of parallel peace deals between Israel, Syria and Lebanon and called on Arab states to support Israeli-Palestinian negotiations and progress on the other tracks by taking bolder steps to foster positive relations throughout the region and to combat violence and extremism.

The group's statement condemned continued violence against both sides, particularly an attack in the occupied West Bank which killed four Israelis on Aug. 31 and was claimed by the Islamist Palestinian group Hamas, which has rejected the current peace negotiations.

It also repeated calls on Arab states to step up financial support for the fledgling Palestinian Authority, which needs much more help as it seeks to take on more of the attributes of full statehood in advance of a possible peace deal.

The statement committed the group -- the main guarantors of any future Middle East peace deal -- to remain involved in the negotiations, and said it supported holding an international Mideast peace conference in Moscow at a date yet to be determined.

A diplomatic source said Israeli and Palestinian leaders met in New York on Monday, a week after the latest round of Middle East peace talks ended without visible signs of progress on the settlement issue.

Israeli President Shimon Peres, whose position is largely ceremonial, met Palestinian Authority President Mahmoud Abbas on the sidelines of the U.N. General Assembly meeting, the source said.

It remains unclear when Abbas will next hold talks with Netanyahu. They have held two rounds of direct talks since the negotiations resumed on Sept. 2, after a 20-month hiatus. (Reporting by Andrew Quinn, editing by Todd Eastham)