It noted in a statement none of the Israeli forces were wounded in the clash.
The soldiers, members of the elite infantry Golani reconnaissance unit, grabbed three M-16 rifles and a pistol used by the Palestinians, the army added.
The Lions' Den, an emerging Palestinian militant group that claims to rise above traditional factional loyalties and has been blamed for a number of attacks on Israeli targets, identified the three as members.
A statement from the group said the three had engaged in combat after identifying the Israeli ambush, vowing to revenge the "martyrs".
Violence intensified last year, but has worsened in the West Bank -- which Israel has occupied since the Six-Day War of 1967 -- after Prime Minister Benjamin Netanyahu returned to office in December at the head of a hard-right coalition.
Hamas, the Islamic rulers of the Gaza Strip, said the latest deaths would "fuel the great West Bank intifada," or uprising.
Islamic Jihad, another Gaza-based militant group, said the deaths were part of the "all-out war" it argued Israel had launched against the Palestinian people.
"Our people's resistance will remain steadfast," the group said in a statement, "no matter what the sacrifices are."
Several Palestinian armed groups had called for revenge since an Israeli army raid on Tuesday, also in the northern West Bank, killed six Palestinians.
On Wednesday, UN Middle East peace envoy Tor Wennesland urged Israel and the Palestinians to end violence without delay.
"We are in the midst of a cycle of violence that must be stopped immediately," he said in a statement.
The Sunday shoot-out took place a short distance from an Israeli settlement, with the head of the regional Samaria settler council praising the army for "taking out the murderous terrorist squad operating in the area".
"We will continue to live and build here in Samaria and the entire region," Yossi Dagan said in a statement, using the Jewish biblical name for the northern West Bank.
Netanyahu's government has vowed to continue the expansion of West Bank settlements, which are illegal under international law.
Calls for calm
On Thursday, a member of the armed wing of Hamas opened fire outside a Tel Aviv cafe, wounding three men in their 30s before being shot dead.
Hours before, three armed Palestinians were killed in an Israeli military operation in the northern West Bank.
The Tel Aviv attack came just hours after Pentagon chief Lloyd Austin had called for de-escalation ahead of the Muslim fasting month of Ramadan that starts in March and the Jewish holiday of Passover in April.
Austin, following talks with Netanyahu and Israeli Defence Minister Yoav Gallant during a brief visit to Israel, also called on the "Palestinian leadership to combat terrorism and to resume security cooperation and to condemn incitement".
In Beitar Illit, a Jewish settlement in the West Bank southwest of Jerusalem, the army said bomb disposal experts had detonated a suspicious package found on a bus Thursday evening.
A Palestinian from a nearby village was arrested on Saturday for having placed an explosive device on the bus, along with four others suspected of aiding him, the army said.
Since the start of the year, the Israeli-Palestinian conflict has claimed the lives of 81 Palestinian adults and children, including militants and civilians.
Thirteen Israelis, including three children and one policeman, and one Ukrainian civilian have been killed over the same period, according to an AFP tally based on official sources from both sides.