Palestinian leaders condemned the killing and said it could jeopardize nascent Middle East peace negotiations being brokered by the United States.
The Islamist Hamas group named the dead man as Iyad Shilbayeh, saying he was a local commander of their armed wing and vowed to carry on fighting. It accused Israeli soldiers of murdering him in "cold blood" -- a charge rejected by the army.
Hamas claimed responsibility for killing four Israelis last month, ahead of the resumption of peace talks between Israelis and Palestinians, and it was not immediately clear if Shilbayeh was suspected of involvement in those deaths.
Relatives said he was shot dead in his house after troops arrived to arrest him. Soldiers knocked on his door then went inside, and Shilbayeh was heard saying "Who is there?" before three shots were heard, his brother Mohammed told Reuters.
An Israeli spokeswoman said Shilbayeh was shot during a "routine arrest raid" in a Palestinian refugee camp near Tulkarm, a West Bank town known for its militant activity.
She said the soldiers had opened fire after Shilbayeh came toward them despite being told to halt.
Palestinian Prime Minister Salam Fayyad called the killing a "dangerous escalation," saying in a statement that it "jeopardizes the international efforts being exerted to make progress in the peace process."
Fayyad is a member of the Palestinian Authority, which controls the West Bank and is at fierce loggerheads with Hamas.
Hamas denounced the killing as a "despicable crime."
"The resistance will continue and the enemy will not succeed in breaking it," Hamas spokesman Sami Abu Zuhri said in Gaza, a coastal strip some 40-km (25 miles) from the West Bank which is sealed off by Israeli forces.
Hamas said Shilbayeh had served time in Israeli jails and had also been detained 10 times by the Palestinian Authority, adding that he had been released two days ago from a PA prison.
It accused Palestinian President Mahmoud Abbas's party of sharing responsibility for his death.
Hamas has greeted the new peace talks with an upsurge of violence, with militants firing rockets and mortars into Israel from Gaza, which it controls.
Israel has responded with a series of air strikes and tank fire, in which three Palestinian militants have been killed.
(Reporting by Muin Shadid in Tulkarm, Mohammed Assadi in Ramallah and Nidal al-Mughrabi in Gaza; Writing by Allyn Fisher-Ilan; Editing by Crispian Balmer and Noah Barkin)