In the old city of Nablus, an AFP correspondent reported Palestinians trading gunfire with Israeli security forces.
The Palestinian Red Crescent Society said its medics treated 69 people for gunshot wounds across the Nablus area, at least four of them in critical condition.
Israeli prime minister Yair Lapid hailed the raid as a "highly successful, precise action without casualties" among the security forces.
Israeli forces said they launched a shoulder-fired missile at the house and detained four suspects in the raid.
Nabulsi was a commander of the Al-Aqsa Martyrs' Brigade, one of the main militant groups present in the West Bank operating under the ruling Fatah party.
Following the deadly raid, the militant group said "the response will fit the crime".
Hundreds of mourners gathered in Nablus for the funeral procession of the three dead, with some militants firing into the air as the bodies were carried through the crowd.
The Palestinian health ministry identified those killed as Nabulsi, Islam Sabbouh and Hussein Taha.
Jamal Taha said his 16-year-old son was killed while they were walking to work.
"The army was in the old city. My son went ahead of me to the market, he was carrying his food. There was shooting and four of us were injured," he told AFP.
Later Tuesday, the Palestinian health ministry said 17-year-old Moamen Jaber was shot in the chest and killed by Israeli forces in Hebron.
An AFP photographer saw the teen's body at a local hospital following clashes between Palestinians and Israeli soldiers.
In Nablus, heavy gunfire was heard as dozens of Israeli military vehicles brought traffic in one of the West Bank's largest cities to a standstill.
Clashes with the Israeli army also broke out in other parts of the city, as Palestinians hurled stones at the troops.
"A violent clash developed with dozens of rioters who threw stones and threw explosives at the forces, who responded by means of crowd dispersal and shooting. Several injuries were confirmed," the army said.
Security forces have conducted near-daily and often deadly operations in the West Bank in recent months, focusing on militants from the Islamic Jihad group.
Deadly Gaza fighting
On Friday, Israel launched what it called a "pre-emptive" aerial and artillery bombardment of Islamic Jihad positions in the Gaza Strip, leading militants in the coastal enclave to fire more than a thousand rockets in retaliation, according to the army.
An Egypt-brokered ceasefire reached Sunday ended three days of intense fighting that killed 46 Palestinians, 16 of them children, and wounded 360, according to Gaza's health ministry.
Israel's Lapid spoke by telephone with Egyptian President Abdel Fattah al-Sisi on Monday, with the premier praising Cairo for its role in "preserving regional stability and security".
But following the Nablus raid, a spokesman for Palestinian president Mahmud Abbas said Israel is "not interested in calm and stability".
"It's exploiting and killing Palestinians for gains in internal Israeli politics," Nabil Abu Rudeineh said, alluding to a snap Israeli general election called for 1 November.
The Israeli prime minister said Monday the strikes on Gaza had hit the "entire senior military command of Islamic Jihad" in the Palestinian enclave.
Islamic Jihad said 12 of its members had been killed, including commanders Taysir al-Jabari and Khaled Mansour.
Israel insists that some civilians counted in the Palestinian toll were killed by Islamic Jihad rockets that fell short or misfired.