Correction: An earlier version of this story incorrectly attributed six Palestinian deaths to the Israeli operations in the wake of the death of an Israeli settler. The operation referred to resulted in three deaths. The deaths of three other Palestinians referred to in this story were the result of separate circumstances.
Jerusalem (CNN) -- Israeli forces killed six Palestinians in separate incidents in the West Bank and Gaza early Saturday, acts that quickly drew Palestinian condemnation.
The first incident happened in the West Bank city of Nablus, where the Israeli military killed three Palestinians it said were responsible for the death of an Israeli civilian in the West Bank this week.
Israeli forces entered Nablus overnight to locate the suspects and killed them Saturday morning, the Israel Defense Forces (IDF) said. Palestinian medical officials and witnesses confirmed the deaths.
The strike was a joint operation by the Israeli military and Israeli security services, a spokeswoman for the Israeli military said. She said all three men were known militants associated with Fatah militant groups.
Israeli forces found four guns at the place where one of the suspects was killed, the IDF said.
"The Israel Defense Forces will act firmly against those who aspire to harm citizens of the state of Israel and Israeli security forces, and will not rest until those involved in the murderous act are brought to justice," said Maj. Gen. Avi Mizrachi of the IDF.
The IDF blamed the men for the killing Thursday night of Israeli settler Meir Avshalom Hai, who lived in the settlement of Shavei Shomron in the northern West Bank. The 54-year-old father of seven was shot and killed in his car near the entrance to the settlement, said Col. Avi Gill of the Israeli military.
The Israeli military spokeswoman could not say what proof or evidence they had against the three Palestinian suspects, who all lived in Nablus.
Two of the Palestinians, both 40, had been imprisoned in Israel in the past; one of them had been a senior member of the Al Aqsa Martyrs Brigades, the militant wing of the ruling Fatah party in the West Bank, according to the IDF.
The third man, who was 36, had been involved in widespread militant activity and had been an arms dealer and supplier, the IDF said.
Palestinian medical officials in Nablus said two of the men suffered gunshots to both the upper body and the head.
Witnesses near the site of the operations told CNN more than 50 Israeli military vehicles supported dozens of soldiers and that the city became a closed military zone. The witnesses also said it appeared the men could have been arrested rather than killed.
"All three were killed in cold blood," said Dr. Ghassan Hamdan, director of the Palestinian Medical Relief Committee in Nablus, who visited all of the locations where the military operation took place.
"The Israeli military could have easily arrested them but it shows that this was not the intention," Hamdan told CNN. "This was clearly assassination and liquidation of Palestinian people in cold blood. ... My experience and what I saw on the bodies describes that they have been killed in cold blood."
The Israeli military said it could not immediately comment on the allegations.
Hamdan said there was evidence on one of the bodies that the man had been interrogated before being killed, though he did not say what that evidence was.
The operation in Nablus followed a separate incident Saturday morning, in which three Palestinians were killed in an Israeli airstrike along the northern border between Gaza and Israel.
The three men were observed moving along the Palestinian side of the border fence, a spokesman for the Israeli military told CNN. The Israelis fired warning shots but the men continued to move along the fence, at which point an Israeli military aircraft fired at and killed the men, the spokesman said.
The military believed the three men had "intention to carry out a terrorist attack" but could not confirm whether the men were observed carrying weapons or explosives, the spokesman said.
An adviser to Palestinian Authority President Mahmoud Abbas and spokesman for the Palestinian Authority, Nabil Abu Rudeineh, condemned the two incidents.
"The Israeli escalation in the West Bank and Gaza and the return to the policy of assassinations and random killings in virtual excuses shows that the the Israeli government decided to destroy the independence and security of the Palestinian people and is pulling our people into a bloody circle of violence," Rudeineh told CNN.
"The Israeli government should bear the responsibility for the killings and also bear the responsibility for the dead end in moving the peace process forward because of Israel's refusal to stop the policy of settlement and to commit to the references of the peace process," he said.
Rudeineh called on the international community, and especially the U.N. Security Council, U.N. General Assembly and the Middle East quartet of Russia, the United States, European Union and United Nations, to intervene immediately "to stop the crimes of the Israeli occupation."
CNN's Kevin Flower contributed to this report.