The Palestinian health ministry identified the four as Raed Abu Seif, 21, and Saleh Ammar, 19, as well as Amjad Husseiniyah and Nureddin Jarrar, whose ages were not immediately available.
The bodies of Abu Seif and Ammar were seen at the Jenin hospital morgue, while Israeli forces were holding two other bodies.
Late morning, a crowd gathered for the funerals of Abu Seif and Ammar, whose remains were draped in Palestinian flags and carried on makeshift stretchers through the Jenin refugee camp.
The camp was a hotspot during the two Palestinian intifadas against Israel in 1987-1993 and 2000-2005.
UN Middle East peace envoy Tor Wennesland voiced alarm over their killings.
"Alarmed by the incident in which 4 #Palestinians were killed by Israeli Security Forces who reportedly came under fire during an arrest operation in Jenin," he wrote on Twitter, adding that "authorities must swiftly investigate."
The Palestinian presidency condemned a "heinous crime" and held Israel "responsible for the escalation and its repercussions".
"The continuation of the Israeli policy will lead to an explosion of the situation, increased tensions and instability," presidential spokesman Nabil Abu Rudeina warned in a statement.
The Jenin gunfight was the deadliest Israeli-Palestinian violence since the May 21 start of an uneasy ceasefire between Israel and Palestinian militants in Gaza following a deadly 11-day battle.
Hours after the Jenin incident, a rocket was fired from Gaza toward Israel, which intercepted it with the "Iron Dome" missile system, the army said.
No group claimed responsibility for the rocket, the first since the May fighting sparked by clashes in Jerusalem over evictions and police raids of the Al-Aqsa mosque.
Israeli airstrikes killed 260 people, including fighters, in the blockaded enclave, while rockets and mortars from Gaza killed 13 in Israel including a soldier.
Since the UN-mediated ceasefire came into effect, there have been numerous clashes between Israeli forces and Palestinians in the northern occupied West Bank, fuelled by a dispute over a wildcat Israeli settlement.
Residents of the village of Beita have held regular protests since May against dozens of Israeli settlers who built an settlement unauthorised by Israeli authorities on lands Palestinians say belong to Beita and other nearby communities.
Israeli security forces who quelled the protests have killed several Palestinians and left hundreds more injured.
The Eviatar settlement was evacuated in early July but Israeli troops continue to guard the site and the homes built on the land while authorities consider whether to approve a permanent community.
Beita residents have vowed to continue their campaign until the army also leaves the outpost.
Israel occupied the West Bank during the 1967 Six-Day War and all Jewish settlements there are considered illegal by most of the international community.
Almost half a million people live in Israeli settlements in the West Bank, alongside 2.8 million Palestinians.
