* Separate incidents in Tel Aviv, occupied West Bank

* Israeli-Palestinian strife over Jerusalem holy site (Releads for soldier's death)

By Jeffrey Heller

JERUSALEM, Nov 10 (Reuters) - An Israeli soldier and a woman were stabbed to death by Palestinians in Tel Aviv and the occupied West Bank on Monday, extending a surge in violence fuelled by strife over access to Jerusalem's holiest site.

Prime Minister Benjamin Netanyahu pledged to crush "terror being directed at all parts of the country" - remarks appearing to clash with Israeli security chiefs' assertions that the tumult did not yet spell a new Intifada, or Palestinian revolt.

The soldier's stabbing at a train station in Tel Aviv, Israel's commercial capital, brought bloodshed to a city that has largely been spared since the last uprising died down in 2005. Police identified the suspected assailant, who was arrested, as a West Bank resident who was in Israel illegally and had no criminal record there.

Hours later, a Palestinian stormed out of a car to stab an Israeli woman to death and wound two other people outside the Jewish settlement of Alon Shvut in the West Bank, police said.

The attacker was shot and wounded by a guard, they added. The militant group Islamic Jihad claimed him as one of its own and an Israeli security official said he had been jailed between 2000 and 2005 for a petrol bomb attack.

Tension has risen anew over Israeli-controlled access to Jerusalem's Al-Aqsa mosque compound, Islam's third holiest site, where biblical Jewish temples once stood.

Stone-throwing protests have erupted in several Arab towns in Israel since Saturday, when police killed an Arab youth who assaulted them. Last week, a Palestinian rammed his car into pedestrians in central Jerusalem, the second such incident in as many weeks, killing two Israelis. Police shot the driver dead.

There was no immediate comment on Monday's stabbings from the U.S.-backed administration of Palestinian President Mahmoud Abbas, which is based in the West Bank, whose peace talks with the Netanyahu government collapsed in April.

Hamas, the Palestinian Islamist group with de facto control over the Gaza Strip, where it fought a war with Israeli forces in July and August, hailed the attacks as "a response to crimes conducted by the occupation (Israel) in Jerusalem and Al-Aqsa".

Israel refers to the Al-Aqsa compound as the Temple Mount and some Jewish nationalists have been stepping up demands to pray there, infuriating Palestinians despite Netanyahu's repeated vow to maintain a decades-old arrangement with Jordan - the compound's custodian since 1924 - that only Muslims may worship there.

Speaking in parliament, Netanyahu said "terror ... is being directed at all parts of the country for a simple reason: the terrorists, the inciters, want to drive us from everywhere".

"As far as they are concerned, we should not be in Jerusalem, Tel Aviv or anywhere. I can promise you one thing - they will not succeed. We will continue to fight terror ... and we will defeat it together," he said.

Jordan blames Israel for the crisis, saying the growth of Jewish settlements on occupied land that Palestinians seek for a state, coupled with increased visits to Al-Aqsa by Jewish ultra-nationalists under police guard, have inflamed passions. (Additional reporting by Dan Williams, Allyn Fisher-Ilan and Nidal al-Mughrabi; Editing by Mark Heinrich and Kevin Liffey)