The Israeli military has said that the three men shot dead in Nablus were behind the killing of an Israeli settler on a West Bank road on Thursday.
It said a ballistic analysis showed that weapons found in the house of Anan Tzubach, one of the dead, were used to murder Meir Avshalom Hai, the settler.
Al-Aqsa Martyrs Brigades was one of two groups to claim responsibility for the shooting.
Family members of the three men said the troops entered without warning and killed all three in cold blood, insisting none had resisted arrest.
The Israeli military confirmed that none of them fired any shots at its soldiers and said only one of them was armed.
Binyamin Netanyahu, the Israeli prime minister, praised the commando operation, telling the cabinet that Israel would "continue to defend aggressively and respond to every attack against Israeli citizens and every rocket strike."
The US has reportedly questioned Israel over the raid.
An official quoted by the Haaretz newspaper said Washington had contacted Uzi Arad, a senior aide to Netanyahu, over the incident.
"We expressed our concern and encouraged both sides to continue their security co-operation," he was quoted as saying.
"We talked to both sides in order to get full information about what happened."
A state of mourning has been announced in Nablus, with shops closed across the city. Thousands of people turned out for the funeral of the men.
Netanyahu told cabinet ministers on Sunday that one of the assassinated had been freed from an Israeli prison, highlighting the risks of the prisoner swap deal Israel is negotiating in a bid to free Gilad Shalit, an Israeli soldier held by Hamas since 2006.
"We want to free captives, but at the same time, we want to minimise the risk to our civilians," Netanyahu said according to a participant in the meeting.
An Israeli military spokeswoman said the three Palestinians killed in the Gaza Strip were suspected of trying to infiltrate from Gaza.
However, a Hamas security source said the three were civilians collecting scrap metal in an industrial zone near the Israeli border.
Palestinian officials accused the Israeli government of attempting to escalate the situation in the Palestinian territories.
"The Israelis have committed a crime that proves they do not want and do not even think about peace with the Palestinians," Nabil Abu Rudaina, a spokesman for the Palestinian presidency, said.
"By committing this, Israel seeks to abort the US and international effort to resume negotiations."