Barghouti has been the subject of a massive man hunt throughout the West Bank after he was involved in a drive-by shooting that left seven people critically wounded and one newborn baby dead.
There were no immediate details on the identity of the assailant.
The Israeli army said it had closed all entrances and exits to Ramallah city in a bid to find the attacker.
A few hours later, Ashraf Naalwa, a Palestinian who was named by the Israeli army as a suspect of murdering two Israelis at the recycling centre where he worked in the Barkan industrial zone of the West Bank, was killed after a two-month manhunt.
The Israeli military has also confirmed that another Palestinian was killed during an arrest attempt in the city of Nablus.
Two Israeli police officers were stabbed in Jerusalem and neutralised the attacker with return fire, the law enforcement agency's press service said. "The security forces are pursuing them, and I hope that there will be news soon on this matter".
He was armed when security forces came to his hideout, the Israel Security Agency said in a statement about his apprehension and death. It said an unspecified number of other suspects were arrested.
Israeli forces also shot dead a Palestinian man in the occupied West Bank last night for his alleged involvement in a Sunday shooting attack near the Ofra settlement.
In Sunday night's attack, assailants in a Palestinian vehicle opened fire at a bus stop outside a West Bank settlement, wounding seven people, including a 21-year-old pregnant woman, before speeding away.
"This is an attack Hamas praised as 'heroic, '" he wrote.
Such attacks have been repeatedly committed by Palestinians and qualified by the Israeli authorities as acts of terrorism.
"The global community bears part of the responsibility for the aggression by the occupation and the settlers because of its silence towards these attacks", said Palestinian government spokesman Youssef Al-Mahmoud.
The Israeli raids come just as a deal had been secured to restore relative calm to another part of the Palestinian territories, the Gaza Strip.
The incident comes as Israeli troops ended a two-month manhunt for a Palestinian wanted in the killing of two Israelis at a West Bank industrial zone in October.
One soldier was lightly injured in the incident, the army said.