The Palestinian Red Crescent said the two men were killed in clashes with the military in Nablus and identified them as Aboud Sobh, 29, and Muhammad Al-Azizi, 22. The rescue service said 19 Palestinians were wounded, including two critically.
Israeli Prime Minister Yair Lapid said the suspects had been wanted for a series of shootings.
“We won’t sit and wait for Israeli citizens to be harmed,” he told a meeting of his Cabinet. “We will go out and harm the terrorists in their homes.”
Nabil Abu Rdeneh, spokesman for Palestinian President Mahmoud Abbas, condemned the violence, saying it was a result of Israel’s occupation of lands Palestinians seek for an independent state.
“The region will remain in a cycle of violence until the occupation is ended and a just peace achieved,” he said.
The military said a violent protest broke out as troops were operating in Nablus, with protesters hurling explosive devices at soldiers and opening fire at them. The soldiers fired back, the military said.
The military said it also operated in a separate area of the West Bank, where another brief exchange of fire took place.
Israeli forces have been carrying out near-daily raids in the West Bank for months, in a bid to quell a spate of attacks by Palestinians on Israelis that has since subsided.
The military has faced resistance during some of those raids, which in several instances have turned deadly.
The Palestinian attacks on Israelis earlier this year killed 19 people. More than 60 Palestinians have been killed by Israeli forces since the start of the year, according to an official Palestinian tally.
The Palestinians want the West Bank, the Gaza Strip and east Jerusalem, territories Israel captured in the 1967 Mideast war, for their hoped-for state.