(Recasts, adds background)

By Arshad Mohammed

JERUSALEM, March 29 (Reuters) - U.S. Secretary of State Condoleezza Rice, beginning three days of talks with Israeli and Palestinian leaders who are seeking to reach a peace deal, said on Saturday she would push to ease West Bank restrictions.

Marred by violence, Israeli travel restrictions and disputes over expanding Jewish settlements in the occupied West Bank, the peace talks have shown little sign of progress four months after they were launched with the aim of reaching a deal before U.S. President George W. Bush leaves office in January.

Rice said the focus would be on discussing practical ways to improve the lives of Palestinians on the West Bank. She had not brought specific U.S. proposals on how to bridge Israel- Palestinian differences on the broader peace effort.

"The improvement of life on the ground is the piece that I think really has to be pushed forward pretty hard," Rice told reporters as she flew to Israel, where she began her talks with Israeli Prime Minister Ehud Olmert.

"I am not coming to insert American ideas into this process," Rice said, describing peace talks led by Israeli Foreign Minister Tzipi Livni and Palestinian ex-premier Ahmed Qurie as "pretty useful" despite the lack of visible progress.

Looming over the peace effort is a split among Palestinians between the Fatah movement, which holds sway over the West Bank, and Hamas, which took control of the Gaza Strip by force last year and seeks the destruction of Israel.

Rice's visit -- her second this month -- aims to assess prospects for diplomatic progress before Bush's expected return to the region in May to mark Israel's 60th anniversary.

On Sunday she will hold separate meetings with Livni and Israeli Defence Minister Ehud Barak, then convene a three-way meeting with Barak and Palestinian Prime Minister Salam Fayyad to discuss ways of easing the movement of people and goods in the West Bank and reviving the Palestinian economy.

CHECKPOINTS

So far Barak has balked at removing major West Bank checkpoints, citing fear of Palestinian suicide bombings. The Palestinians call the hundreds of checkpoints, roadblocks and other barriers a form of collective punishment.

Rice said she would look at the issue of checkpoints. "Obviously there are security issues but we do have to find ways to improve movement," she said.

She will then shuttle between Israeli and Palestinian officials, meeting Abbas in Amman on Sunday, seeing Olmert again on Monday, and then returning to Amman for further talks with the Palestinian president.

She also plans a three-way meeting between Livni and Qurie on Monday.

Rice has said that neither side had done "nearly enough" to carry out the 2003 "road map" peace plan under which Israel is required to halt West Bank settlement activity and uproot settler outposts and the Palestinians to curb militants.

Citing security obligations under the road map, Rice said she hoped to discuss specific ways to expand Fayyad's law and order campaign beyond the West Bank city of Nablus.

"That both gets at one aspect of the road map, which is increasing Palestinian security competence and authority, and it begins to get at the questions of improvement of movement and access and economic life for people," Rice said.

Barak said last week he would let Fayyad deploy security forces, undergoing training in Jordan under a U.S.-funded programme, in the northern West Bank city of Jenin.

Rice's last visit was followed by a lull in fighting between Israel and Hamas Islamists who control the Gaza Strip, though Palestinian hospital officials said Israeli troops killed two gunmen there on Saturday. Gazan militants have also continued to fire rockets over the border.

Because Hamas is shunned by Israel and the United States, Egypt has taken on the role of mediator, seeking an informal deal to curb both Israeli military raids and the rocket fire.

"Obviously we are continuing to try to find an answer for Gaza, where there needs to be an end to the rocket attacks on Israel and where we need to find solutions -- sustainable solutions -- for the humanitarian situation," Rice said.

But when asked if she was more amenable to a formal Gaza cease-fire agreement, Rice said: "No". (Writing by Adam Entous and Arshad Mohammed; Editing by Dan Williams and Richard Balmforth)

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