A Hamas statement said al-Natsheh, 25, was a member from the group, and said he fought the soldiers for 12 hours before he was killed.
The group's armed wing, the Izz el-Din Brigade, vowed to avenge Natsheh's killing.
"Our response will be swift and painful," it said in a statement.
An Israeli army spokeswoman said soldiers clashed with a group of armed men in the city, killing a fighter. She declined to give further details.
The Israeli military confirmed it carried out the raid, saying that during the exchange of fire, troops heard explosions from inside the house, presumably from bombs stored inside.
Palestinian security officials said al-Natsheh was wanted by Israel for involvement in suicide bombings.
Israel and Hamas are observing a ceasefire in the Hamas-ruled Gaza Strip. But the agreement does not apply in the West Bank, ruled by Mahmoud Abbas, the Palestinian president and leader of Fatah, Hamas's rival.
Army of Islam targeted
Meanwhile, in Gaza City, clashes broke out early on Sunday Hamas-run security forces continued a crackdown on rival Palestinian factions after a deadly bombing, witnesses said.
The fighting erupted overnight when Hamas-run police moved to arrest members of the Army of Islam, a small group believed to be linked to al-Qaeda.
Witnesses said they heard heavy exchanges of gunfire and explosions in which several people were wounded, including fighters and police, but medical officials were not immediately able toconfirm the reports.
The clashes came as Hamas cracked down on rival groups suspected of planting a bomb on Friday night that killed five commanders and a five-year-old girl.
Hamas blamed the attack near Gaza City on Fatah, which it accused of trying to undermine its rule.
Since the explosion Hamas-run forces have arrested more than 200 people, security officials said, most of them members of Fatah, which was largely expelled from Gaza when Hamas took over.
Security forces have also raided some 40 offices, sporting clubs and charities, most of them linked to Fatah, confiscating computers and documents, according to the independent Palestinian Centre for Human Rights.