An Islamic Jihad official said Karkur belonged to the group.
Al Jazeera's correspondent Nour Odeh said that after the firefight, a bulldozer began to demolish the house without any forewarning, and recovered the body from the rubble.
An Israeli army spokesman acknowledged that troops were operating in Saida, while a spokeswoman said she was looking into the incident.
Israeli forces also carried out raids in several other towns in the West Bank on Wednesday.
The raids took place in Jenin and Qalqiliya besides Tulkarem.
So far, residents of these towns and surrounding villages report that Israeli forces have detained at least 12 Palestinians, Odeh said.
Large operation
In Qalqiliya, the Israelis were involved in a large military operation, deploying in all its neighbourhoods to conduct random searches of residents' homes, Al Jazeera said.
Wednesday's death brings to 6,310 the number of people killed since the start of the second Palestinian uprising in September 2000, the vast majority of them Palestinians, according to a separate AFP count.
Since the Israelis and Palestinians revived their peace talks in late November after a seven-year freeze, at least 347 people have died in violence between the two sides, most of them Gaza fighters, according to an AFP tally.
Al Jazeera boycott
In another development, Israel has decided to boycott Al Jazeera over what it called biased coverage of events in the Gaza Strip, according to an Israeli radio station.
The Israeli foreign ministry was reportedly sending a letter to Al Jazeera intimating its decision, but there has been no official confirmation.
Walid al-Umari, Al Jazeera's Palestine bureau chief, said the decision was part of a campaign against the channel, backed by Israel's foreign ministry.
He said: "A state that respects the freedom of expression or claims that it is democratic should not limit the movement of press teams.
"I dare any Israeli official to bring up what they call incitement or lies reported by Al Jazeera. What we reported were real facts on the ground."
Israeli officials will stop giving interviews to Al Jazeera's correspondents, who will also not be allowed to enter government departments, the radio station said.