JERUSALEM (Reuters) - Israel agreed on Thursday to give Palestinian security forces a freer hand to operate in four West Bank cities and to limit its own military activities there in a U.S.-backed move to bolster President Mahmoud Abbas.

Palestinian officials said the changes were inadequate because the Israeli army still reserved the right to re-enter the cities of Qalqilya, Ramallah, Bethlehem and Jericho to counter what it called any "urgent" threats by militants.

The announcement coincided with efforts by Israeli Prime Minister Benjamin Netanyahu to ease tensions with U.S. President Barack Obama over stalled peacemaking with the Palestinians.

Israel has rebuffed U.S. calls for a halt to Jewish settlement building in the occupied West Bank. On Monday, Israeli Defense Minister Ehud Barak will meet Obama's Middle East envoy, George Mitchell, in Washington to try to narrow differences.

"As of today, Palestinian security forces will be able to operate freely in the cities," an Israeli military official said. Israeli troops would still be able to operate within those cities, battlegrounds during a Palestinian uprising that began in 2000, "in cases of urgent security need," he added.

A statement issued later by the Israeli army said that "responsibility for maintaining security in the region has not been transferred" to security forces loyal to Abbas, whose Western-backed government is based in Ramallah.

Officials said the changes agreed to by Israel would give Abbas' forces greater freedom of movement around the clock. Until now, Israel limited those movements, particularly at night.

But senior Western diplomats briefed by the Israeli government said the decision to ease restrictions would be re-evaluated after a week.

More than 1,600 security men loyal to Abbas have undergone U.S.-funded training since January 2008. They are derided as collaborators by Hamas Islamists who seized control of the Gaza Strip in 2007 after routing Abbas' forces there.

Israel has slowly come to back the U.S. training program as a test of Abbas' ability to rein in militants, as demanded in a 2003 peace "road map" for establishing a Palestinian state.

Abbas has ruled out resuming peace talks with Israel until it halts settlement activity, also required under the road map.

SECURITY RESPONSIBILITY

An Israeli security source said the army would "act as little as possible to allow the Palestinians to take more initiative and responsibility over their own security."

Israeli forces would stay out of the four cities except "in circumstances of 'ticking bombs,' or a planned attack" against Israelis, the Israeli security source said.

The senior Palestinian security official countered, "If there is to be a change, they (Israeli troops) should stop the incursions, not enter under the pretext of 'ticking bombs.'"The official, speaking on condition of anonymity, called the move a public relations "sham." He said Israel should halt incursions without exception.

The changes set out by Israel fell far short of Palestinian demands it pull its forces back to positions they held before the outbreak of the uprising.

In Washington, State Department spokesman Ian Kelly welcomed the Israeli moves as "positive steps," saying they included removing some Israeli checkpoints to make it easier for Palestinians to get around but that more needed to be done.

The spokesman also said that Israel had "legitimate" security concerns that had to be respected.

Israel has been reducing its presence in parts of the West Bank, where anti-Israeli violence has declined. But the army still carries out routine patrols and occasional arrest raids.

Under U.S. pressure, Israel has taken down some West Bank checkpoints, including one at the entrance to Jericho. But hundreds more remain, restricting Palestinian travel and trade.

Israel says the changes were meant to bolster Abbas in his power struggle with Hamas, which won a 2006 Palestinian election but is shunned by Western powers for refusing to renounce violence and for rejecting Israel's right to exist.

Israel informed the Palestinians it would limit army operations in the four cities at a meeting of senior officers on Wednesday. A senior Western security source said other West Bank cities could be added later.

U.S. and Israeli security officials have voiced increasing confidence in Abbas' security forces, which carried out deadly raids against Hamas militants in Qalqilya earlier this month.