In the first raid Palestinian security officials say soldiers encircled a building next to Palestinian intelligence headquarters in Jenin on Sunday.
Gunshots were heard and the bloodstained body of Ali Jabarin, a former member of the al-Aqsa Martyrs' Brigades, was seen lying in the street immediately after the shooting.
Elsewhere six other Palestinians were killed in the town of Qabatiya, south of Jenin, during a raid which ended with the Israeli soldiers bulldozing a house which had been the focus of the fighting.
Security sources said that at least one of the victims was a member of Islamic Jihad.
Mahmoud Abbas, the Palestincian president, denounced the raids calling on the Middle East Quartet to intervene and demand an immediate halt to Israeli attacks.
Abbas was travelling to Russia on Sunday for talks in the Black Sea resort of Sochi with Vladimir Putin, the Russian president.
Israeli troops opened fire on
Israeli military sources confirmed the clashes, but were unable to comment on the casualties.
The army said that in both places troops seeking to carry out arrests were fired upon and returned fire.
Palestinian security sources said the Israeli raid was apparently targeted at Mahmoud Saadi, the overall leader of Islamic Jihad in the Jenin area.
Saadi was hit in the chest and legs but his injuries were not thought to be life-threatening, the sources said.
Sunday's raids came as the Israeli military said it had intercepted a boat smuggling explosives into the Palestinian territories.
An Israeli naval vessel intercepted the boat off the coast of Gaza, confiscating several hundred kilograms of military-grade explosives and mines, officials said.