The shootout came after militants offered to halt rocket attacks
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Israeli soldiers have killed three Palestinian militants in operations near the West Bank city of Jenin.
The incidents occurred late on Sunday and overnight on Monday, hours after Islamic Jihad said it would end an exchange of fire in the Gaza Strip if Israel did the same.
The shootings took place in Qabatiya, the home town of a suicide bomber who killed five Israelis on Wednesday.
A week of violence has now also left 12 Palestinians dead.
Early on Monday, Palestinian militants in the Gaza Strip fired missiles into Israel, though no casualties or damage are reported.
Revenge threat
The Palestinian security sources said Israeli troops surrounded the hideout of an Islamic Jihad militant in Qabatiya at sunset on Sunday.
Witnesses described an Israeli force including jeeps, tanks and helicopters, and a prolonged gun fight.
Two militants tried to flee the house and fired on troops, who fired back and killed them.
In a separate incident in Qabatiyeh, the Israeli military said its troops opened fire on three militants planting a bomb, killing one.
Israel has yet to comment on the West Bank shootout
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The BBC's Jon Leyne in Jerusalem says the shootout came just as efforts to calm a week of violence seemed to be bearing fruit.
Earlier in the day, it appeared a tenuous agreement had been reached to end rocket attacks from Gaza on Israel.
A leader of Islamic Jihad, Khaled al-Batsh, told the BBC the group would stop firing if Israel stopped what he called its aggression.
But our correspondent says that must be thrown into question, and already one senior figure in Islamic Jihad has threatened revenge.
Israel had not responded officially to the ceasefire but there had been no exchange of fire in Gaza since Saturday.
This week's violence flared with the killing of an Islamic Jihad chief on Monday.
Islamic Jihad said it carried out Wednesday's suicide bombing in Hadera in revenge.
Nine Palestinians died in Israeli air strikes on Thursday and Friday which the army said were targeting Palestinian militants.
Israeli Defence Minister Shaul Mofaz has said Israel's strikes were aimed at wiping out Islamic Jihad's ability to carry out suicide bombings.
Mr Batsh did not say the group would halt suicide bombings.