Family members identified the dead man as Muhammad Abu Haznah, 28, a member of the Islamic Jihad group.
Israeli security officials said the man was behind the recent Tel Aviv bombing that killed five Israelis.
They said he was part of a cell that had also built a car bomb the Israelis disarmed last week and was planning further attacks.
Aljazeera's correspondent in Jenin reported that Israeli forces entered the village of al-Nazla al-Wista in northern Tulkaram on Thursday morning.
After surrounding Haznah's house, the troops sent a dog in to flush him out, the army said.
The Israeli army said the activist shot and killed the dog, then opened fire on the soldiers.
The troops then destroyed the building, killing Haznah inside.
All the other residents left the building before it was demolished.
In searches of the rubble the soldiers found Haznah's body and a pistol, the military said.
At a summit last month in which Israeli and Palestinian leaders declared a halt to the violence, Israel said it would not target Palestinian activists unless they were about to carry out an attack.
Relations between Israelis and Palestinians are already tense because of an impasse over Israel's transfer of West Bank towns to Palestinian control.
"Israel should let the Palestinian security forces do their job in these areas"
The killing could deepen the discord because Palestinian activists have conditioned halting violence on Israel's ending its hunts for Palestinian wanted men.
"We believe that the Israelis have committed to stop violence against Palestinians anywhere; these actions are only adding fuel to fire," Palestinian negotiator Saib Uraiqat said.
"Israel should let the Palestinian security forces do their job in these areas."
A spat over the transfer of the quiet town of Jericho to Palestinian security control was already threatening to undermine the month-old truce.
Israel has refused to take down its roadblocks north and south of the ancient town, as the Palestinians have demanded.
Palestinian Authority President Mahmud Abbas and Israeli Defence Minister Shaul Mofaz failed to settle the disagreement in talks on Tuesday, and two meetings of security commanders on Wednesday were no more successful.
The unexpected deadlock raised concerns that the two sides would have trouble working out thornier issues down the road.
Washington's new envoy, William Ward, a US Army general, was due to take up his new post on Thursday, and spokesman for the US embassy in Tel Aviv Paul Patin raised the possibility that Ward would intervene in the dispute.
Ahmad Quraya says Israel is
dragging its feet on the peace plan
"Security coordination is his brief," Patin said.
Palestinian Prime Minister Ahmad Quraya accused Israel of foot-dragging, and the Hamas resistance group warned that Israel "would be held fully responsible for the consequences".
The disagreement over Jericho appears to focus mostly on a luxury casino and hotel just outside the town.
Built in the heyday of Israeli-Palestinian peacemaking in the mid-1990s, the Oasis casino was forced to close after the outbreak of violence in 2000.
"Without lifting the roadblocks, the handover will be meaningless"
Most customers were Israelis, who flocked to Jericho
, just 30km from Jerusalem
, because casino gambling is illegal in Israel
A month after the start of fighting, Israel banned its citizens from entering Palestinian areas, and the casino took some gunfire.
With relations between the two sides improved since the death of longtime Palestinian leader Yasir Arafat, some Palestinians in Jericho are hoping that the Israelis will come back - restoring jobs and boosting the town's battered economy.
But the Israelis do not think the time is right. The ban on Israeli citizens entering Palestinian areas is still in force and all that would stop them from streaming to the casino again is a roadblock the Palestinians want removed.
But the Israelis say that Vered Yericho, a nearby Jewish settlement of 160 residents, would be vulnerable to attacks if the roadblock were removed.
"Without lifting the roadblocks, the handover will be meaningless," said Uraiqat, who lives in Jericho.