By Crispian Balmer and Ali Sawafta

JERUSALEM (Reuters) - Israeli and Palestinian negotiators held a new round of talks on Monday, picking up the tempo of their meetings at the request of the United States in the face of widespread skepticism that they will ever reach a deal.

The two sides resumed direct peace negotiations in late July after three years of stalemate and have conducted a series of discussions far from the gaze of the media over recent weeks, without any outward hint of the slightest breakthrough.

Just as for much of the last 20 years, the same problems continue to snarl progress towards a deal, with Israelis and Palestinians at loggerheads over how to divide the land and over their future security arrangements - among other things.

Palestinian President Mahmoud Abbas held a rare meeting with a group of Israeli parliamentarians on Monday, warning that this could be the last chance to reach a deal to end decades of conflict and create two independent states living side-by-side.

An uncompromising speech by Israeli Prime Minister Benjamin Netanyahu on Sunday underscored pessimism prevailing in both camps, with members of the Israeli leader's own coalition openly campaigning for an end to the so-called peace process.

However, a senior Palestinian official told Reuters that the talks were intensifying, with the negotiating teams agreeing to meet for up to eight hours a day and to see one another more regularly than at the start of their latest diplomatic drive.

"As the Americans requested, we are upping the tempo of the discussions," the official said, adding that Washington would evaluate the situation in the next two months and see how to narrow the inevitable differences.

"So far we have achieved nothing," he said.

For the last two months, the two sides met once or twice a week, sometimes only for a couple of hours a time, raising eyebrows among foreign diplomats, who questioned how the U.S. goal of reaching a full accord by April could ever be met.

"If they are really serious about getting a result within nine months, then they should be meeting every day," said one senior diplomat in Jerusalem, who declined to be named.

CLASHING NARRATIVES

Netanyahu on Sunday pinned blame for the continued impasse on a refusal by Palestinians to recognize Israel as a Jewish state and said they would have to abandon their demand for refugees and their descendants to return to Israel.

His speech went down well with hardliners and supporters of the Jewish settlements that dot the occupied West Bank. Settlers fear that Netanyahu might buckle under international pressure and give Palestinians most of the land seized in the 1967 war.

"Probably the best speech by Netanyahu as PM," Dani Dayan, a former settler leader, said appreciatively on Twitter.

A senior Palestinian official, Yasser Abed Rabbo, dismissed the speech as part of a "political game". He also criticized chief Israeli negotiator Tzipi Livni, who suggested at the weekend that the talks could go on beyond the April deadline.

"This is a clear sign that Israel wants to draw out the process of negotiations for as long as possible so that it can evade international pressure and American disfavor," he told Voice of Palestine radio.

Palestinian leaders have often said continued settlement expansion on land they seek for a state poses the main obstacle to a peace agreement.

Striking a more upbeat tone in his meeting with mainly opposition Israeli politicians, Abbas said he still believed it was possible to strike a comprehensive accord by April.

"I'll say what (U.S. Secretary of State) Kerry has said, that I fear this could be the last chance for peace, which is terrifying. This is why we must work with all our effort to reach peace, because in the unknown, there is great danger."

(Additional reporting by Noah Browning in Ramallah and Maayan Lubell in Jerusalem; Editing by Mark Heinrich)