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 first incident, the soldier's stabbing at a Tel Aviv train station, brought bloodshed to the Israeli commercial capital that has largely been spared since the previous uprising died down in 2005. Police identified the suspected assailant, who was arrested, as a resident of the occupied West Bank who was in Israel illegally and had not previously been arrested.
Hours later, a Palestinian stormed out of a car to stab three people outside the Jewish settlement of Alon Shvut in the West Bank, killing the woman and wounded two other people, police said. The attacker was shot and wounded by a guard.
The militant group Islamic Jihad claimed him as its member and an Israeli security official said he had been jailed in Israel between 2000 and 2005 for a petrol bomb attack.
Israeli-Palestinian bloodshed 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 and whose peace talks with the Netanyahu government collapsed in April.
Hamas, the Palestinian Islamist group with de facto rule over the Gaza Strip where it fought a July-August war with Israeli forces, hailed the attacks as "a response to crimes conducted by the occupation (Israel) in Jerusalem and Al-Aqsa".
Jews refer 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 promise to maintain a decades-old arrangement with Jordan - the compound's custodian since 1924 - for Muslim-only worship.
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 rapid growth of Jewish settlements on occupied land that Palestinians seek for a state, coupled with vocal demands by rightist Israelis for more access to the Jerusalem holy site, have inflamed passions.
