By Dan Williams

JERUSALEM (Reuters) - A Palestinian stabbed and critically wounded an Israeli soldier on Wednesday and was shot dead by troops, the army and a hospital official said, a day after a visit by U.S. Secretary of State John Kerry to explore how to end eight weeks of violence.

The attack occurred in the Israeli-occupied West Bank at a road junction near a cluster of Palestinian villages and Jewish settlements. The army said the soldier was critically hurt and a an official at Shaare Zedek hospital in Jerusalem said the Palestinian assailant died on the operating table.

Israeli media reported later that a top military officer said senior ministers should consider easing certain measures for Palestinians to reduce tensions, such as arming security forces and giving them armored vehicles to quell the violence.

Further proposals were the release of some prisoners and easing of travel and work restrictions. The officer, who was not identified, said the military viewed the current violence as a limited uprising that could last for months.

But media pundits predicted that Israeli Prime Minister Benjamin Netanyahu and his rightist ministers would reject the proposals. Israeli officials have stated that the Palestinians needed to show a willingness to confront the violence.

Eighty-eight Palestinians have been killed since Oct. 1, some while carrying out assaults and others in clashes with Israeli forces. Many of them were teenagers. Nineteen Israelis and an American have been killed in the Palestinian attacks.

Ibrahim Dawoud, 16,was the latest Palestinian fatality announced. He died of wounds suffered in a clash with Israeli troops in the West Bank city of Ramallah two weeks ago, the Palestinian health ministry said.

The violence, fueled in part by Muslim agitation over increased Jewish visits to East Jerusalem's al-Aqsa mosque compound - Islam's third holiest site and also revered by Jews as the location of two biblical-era temples, prompted Kerry to come and sound out both sides on Tuesday.

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With his bid to shepherd talks on a Palestinian state in Israeli-occupied territory frozen since mid-2014, Kerry said his latest mission had the more limited aim of lowering tension.

But there was no indication that any headway was made in his meetings with Netanyahu and Palestinian President Mahmoud Abbas.

A Palestinian official, who asked not to be identified, said Kerry had asked Abbas to try to achieve at least a week of calm to persuade Netanyahu to pursue confidence-building measures.

These would include giving the Palestinian Authority self-rule powers in parts of the West Bank where Israel maintains sole security and administrative control.

Kerry, arriving back in the United States on Wednesday, said Israeli and Palestinian leaders had reached a pivotal point and it was now up to them to make important decisions that will lead to lasting peace.

(Additional reporting by Ori Lewis, Ali Sawafta in Ramallah and Lesley Wroughton in Boston; Writing by Dan Williams and Ori Lewis; Editing by Jeffrey Heller and Mark Heinrich)