The Palestinian Red Crescent Society said in a statement that its crew “removed the bodies of two martyrs from the old city of Nablus.”
According to the Palestinian news agency Wafa, the two youths who died were Hamza Maqbool and Khairi Shaheen.
Israeli troops cordoned off a house before shooting dead the men, the news agency said.
According to the Israeli military, the men are suspected of having shot at the police this week.
Three other people were also injured, Al Jazeera TV reported.
Earlier, eyewitnesses told Anadolu Agency that Israeli special forces had stormed the old town of Nablus, sparking clashes with Palestinian gunmen.
These witnesses saw Israeli military reinforcements entering the city from Al-Quds Street towards the Old City.
The incident came less than two days after an Israeli army attack on the Jenin refugee camp that killed 12 Palestinians and wounded 140 others, 30 of them seriously.
The attack was the largest Israeli attack on the West Bank in more than 20 years.
Since June 2021, Israel has been carrying out raids and killings of Palestinians in the West Bank on an almost daily basis.
Authorities said the move was an attempt to crack down on growing armed resistance.