Israeli forces have made near-daily raids across the territory in recent months, many of them deadly, following a series of lethal attacks on Israelis.
The Palestinian health ministry said three people were killed “by bullets from the Israeli occupation during its aggression in Jenin at dawn today”.
The Israeli military said troops entered Jenin to detain people “suspected of involvement in terrorist activity”.
“The soldiers operated while being targeted with direct fire and responded with live fire,” the army said in a statement.
The military did not respond to AFP’s request for comment on allegations that soldiers fired on an ambulance transporting one of the wounded.
The Islamic Jihad militant group said their fighters were engaged in “fierce clashes” with Israeli forces in Jenin.
Jenin’s Ibn Sina hospital identified the dead as Atta Shalabi, Sidqi Zakarneh and Tariq Damej.
The Israeli army said it had carried out multiple operations across the West Bank overnight to arrest wanted suspects in cities including Bethlehem and Ramallah.
Palestinian towns and cities in the West Bank are nominally under the control of the Palestinian Authority and its security forces.
International alarm
A surge in bloodshed this year has seen at least 150 Palestinians and 26 Israelis killed across Israel and the West Bank.
The toll includes more than 40 Palestinians killed during Israeli operations in the Jenin area, among them children as young as 12 and veteran Palestinian-American journalist Shireen Abu Akleh as well as militants.
The situation has alarmed the international community.
The European Union said Saturday it was “greatly concerned about the increasing level of violence”.
A US State Department spokesman called “for all parties to do everything in their power to de-escalate the situation”.