The men died after Israeli forces fired on their vehicle near Al Tur Gate, the official Palestinian news agency Wafa said on Tuesday.
The Israeli army said it “neutralised” three Palestinians who shot at troops in the city's Samaritan district.
One of the men exited the vehicle and opened fire at soldiers on defence patrol, the army said.
Some Palestinian outlets reported that the men were killed in an “ambush” after an attempted attack by militants on Israeli troops near a Jewish settlement overlooking Nablus.
Palestinian ambulances were prevented from reaching the scene, Wafa reported, while other local outlets cited witnesses claiming the men were taken from the scene by Israeli ambulances.
The Palestinian health ministry said it was informed of the deaths of three people by the General Authority for Civil Affairs, which liaises with Israeli authorities.
It says the identities of the victims are unknown.
Soldiers seized the vehicle and closed off access to the area for residents, Wafa reported. It added that journalists and medics were banned from the site.
Violence has become commonplace in Nablus, one of two major flashpoint cities in the occupied West Bank, over the past year amid almost-daily lethal Israeli raids.
The army claims its targets are militant groups that are plotting or are responsible for attacks in Israel, including the Nablus-based Lion's Den group.
However, civilians and children are regularly among the dead.
This year is the bloodiest in the Israeli-Palestinian conflict in over a decade.
More than 150 Palestinians have been killed since the start of 2023 in the West Bank and East Jerusalem, according to the AP, about half of whom were affiliated with militant groups.
An 18-year-old Palestinian was shot dead on Saturday after an attempted car ramming, a day after another teenager was shot and killed by Israeli forces near Ramallah.
The army said masked suspects “threw stones and rocks” at soldiers but gave no further details.
One person was killed and at least four wounded in Nablus on Thursday.
Right-wing ministers in Israel's government have also contributed to heightened tension in the region, calling for the rapid expansion of Israeli settlements in the West Bank and harsher action against suspected Palestinian militants.
The Palestinians want to establish an independent state in the West Bank, East Jerusalem and Gaza, territories Israel occupied in the 1967 war.
US-sponsored statehood talks collapsed in 2014 and show no sign of revival. Israel has maintained military rule over millions of Palestinians and expanded West Bank settlements, which most countries deem illegal.