“Two citizens arrived at the emergency department, shot by the Israeli army, and died shortly afterwards, succumbing to their injuries,” a source at the hospital was quoted as saying by local media.
The bodies of the two other men, one identified as Noor Jarrar and the other as Amjad Iyad Azmi, were taken by Israeli forces, sources said.
The governor of Jenin confirmed the deaths.
At least two other Palestinians were arrested. One was shot in the hand and the other, identified as Mohammed Abu Zina, was taken from his home during the raid.
Meanwhile, funeral processions began for the slain men in the Jenin refugee camp.
Nearly half a million people live in illegal Israeli settlements in the occupied West Bank, alongside 2.8 million Palestinians.
Palestinians have staged near-daily protests in Beita since May to voice anger at a nearby illegal Israeli settler outpost.
The settlement was evacuated in early July but Israeli army troops remain stationed there while authorities deliberate on its fate. If the settlement is approved, its founders will be allowed to take up residence there more permanently.
Beita’s residents have vowed to continue their campaign until the army also leaves the outpost.
The occupied West Bank is part of the territory where a Palestinian state is envisaged under the two-state solution.
Israel occupied the West Bank during the 1967 War and all settlements there are considered illegal by most of the international community.
Israeli forces often carry out raids in various areas across the West Bank, where they detain, and often kill, Palestinians.