The sources added that a Palestinian civilian in his seventies was shot to death as he left his home and that three other group members were injured.
IDF officials confirmed that military forces had operated in the West Bank city on Tuesday morning.
The Palestinians reported that large IDF forces entered the old city of Nablus on Monday night and clashed with wanted members of the al-Aqsa Martyrs' Brigades, Fatah's military wing.
According to the source, Shakher al-Wazir, a Palestinian civilian in his seventies, was killed in the exchanges of fire after being shot near his house. The Palestinians claimed that he was forced to leave his home due to the clashes and was caught in the exchanges of fire between the soldiers and the gunmen hiding in the building.
Three Fatah members were injured in the incident, two of them critically. One of them, Abed Shinawi, was a senior member of Fatah's military wing.
IDF sources reported that "the forces were engaged in the detention of wanted Palestinians, who opened fire at the troops in several different incidents. The soldiers fired back at the shooters, and there were no injuries among the soldiers."
Three wanted Palestinians were arrested and taken in for questioning by security forces.
The forces were encircling a building where fugitives were hiding. According to the military sources, during the clashes an injured Palestinian came out from one of the buildings and was evacuated to hospital by a Red Crescent emergency crew, which later announced that the man died of his wounds.
"We do not know if the man was hit by IDF fire or by the gunmen," an IDF source said.
A senior al-Aqsa Brigades member in Nablus told Ynet in response to the incident that the raid proved that Israel was not satisfied with the organization's commitment to the ceasefire.
According to the man, Israel is trying to lead Fatah to resume its terror attacks.
"Our current stance is to stick to the demands of our leadership, headed by President Mahmoud Abbas. However, the IDF's ongoing operations will result in painful responses against Israel," he said.
Efrat Weiss contributed to this report