By John Irish

NEW YORK (Reuters) - The "Quartet" of Middle East peace mediators said on Friday it was strongly opposed to Israel's ongoing settlement activity, warning that it risked ending the chance of a two-state solution with the Palestinians.

Peace talks, envisaging a Palestinian state in territory Israel captured in a 1967 war, collapsed two years ago after nine months of largely fruitless discussions sponsored by the United States.

The acid political climate between Israelis and Palestinians makes progress unlikely. Both Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas showed no signs of a rapprochement during their speeches at the annual U.N. gathering of world leaders.

"The Quartet emphasized its strong opposition to ongoing settlement activity, which is an obstacle to peace, and expressed its grave concern that the acceleration of settlement construction and expansion ... (is) steadily eroding the viability of the two-state solution," the Quartet said in a statement after meeting on the sidelines of the U.N. General Assembly.

The group, which comprises the United States, the United Nations, the European Union and Russia, issued a report in July calling on Israel to stop its policy of building settlements on occupied land and restricting Palestinian development, but the activity has shown no signs of abating.

The Quartet also condemned a resurgence of violence. It urged both sides to de-escalate tensions and show restraint.

With U.S. efforts to broker a deal frozen, France and Egypt have tried to revive interest, warning that letting the matter drift even during a U.S. election year was counterproductive.

After outlining for the Quartet efforts to bring the two sides back to the table by year-end, Foreign Minister Jean-Marc Ayrault said that while the path to peace was narrowing, it still existed.

"It's true that listening to Abbas and Netanyahu's speeches at the U.N., you can't say their views are converging ... but we can't accept the fait accompli. That would lead to despair and violence," he said.

Palestinians say Israeli settlement expansion in occupied territory is dimming any prospect for the viable state they seek. Israel has demanded tighter security measures from the Palestinians and a crackdown on militants responsible for a string of stabbings and shootings against Israelis.

The CIA Factbook online says about 371,000 Israelis live in settlements scattered among an estimated 2.7 million Palestinians in the West Bank, captured by Israel in the 1967 war. The figures exclude East Jerusalem, which both sides claim.

(Reporting by John Irish; Editing by Howard Goller)