The killings possibly signal an end to the period of calm, with al-Aqsa Martyrs Brigades leader in Jenin, Zakaria al-Zubaydi, on Thursday vowing to retaliate.
The dead men have been identified as a leader of al-Aqsa Martyrs Brigades in Jenin, Samir al-Saadi, and two activists of the Islamic Jihad movement and the Popular Front for the Liberation of Palestine (PFLP) respectively.
The clashes erupted early on Thursday when Israeli forces surrounded the men at the western gate of Barqin town, near Jenin.
Subsequently, Aljazeera's correspondent Ali al-Sumodi quoted al-Zubaydi as saying the retaliation would take place deep in 1948 lands.
"When we announced this period of calm, we said that any assassination operation against al-Aqsa Martyrs Brigades leaders and activists would cancel this agreement," al-Zubaidi said.
Al-Aqsa Martyrs Brigades has
announced an end to the truce
"Let Sharon know that we will retaliate for this criminal action in Jenin city.
"The government of this Zionist enemy knows that Jenin city represents a belt of fire that would burn the Zionist enemy deep in Zionist areas, inside our lands occupied in 1948."
Agencies reported quoting Palestinian witnesses that the fighters had hid in an olive tree when Israeli troops shot them.
Soldiers also arrested 12 suspected fighters in raids conducted in the Jenin, Nablus and Bethlehem areas of the West Bank, the Israeli army said.
Reporting from Jenin, Aljazeera's correspondent, said the town was seething with anger as residents and fighters flocked to the hospital to prepare for the funeral of the three slain fighters.
A huge funeral procession was expected to be held on Thursday after the noon prayers, he added.
Following the killings, al-Aqsa Martyrs Brigades' al-Zubaydi announced the group's decision to end the period of calm with Israel, al-Sumodi reported.
The ongoing Israeli aggression had broken it, he quoted al-Zubaydi as saying.
For its part, Islamic Jihad's military wing al-Quds Brigades warned that its response to the Jenin killings would be fierce and that it would seriously reconsider its commitment to the period of calm.
"Let Sharon know that we would retaliate for this criminal action in Jenin city"
Al-Aqsa Martyrs Brigades' Jenin leader
Speaking to al-Sumodi, the two groups said their threats meant a return to operations inside Israel and other areas as their patience had run thin.
Thursday's killings took place against the backdrop of a massive search-and-arrest operation launched by Israeli forces in the area, resulting in the detention of several Palestinians.
In the Gaza Strip, meanwhile, Palestinian police blew up the largest synagogue building of the demolished Neve Dekalim settlement, planting explosives, then detonating them, which destroyed the building, witnesses said.
It was not the first synagogue structure to be demolished by Palestinians but the others were bulldozed rather than blown up.
The Gaza incident came shortly after Israeli aircraft fired missiles at targets in Gaza, knocking out power to thousands of Palestinians for a second straight day.