Israel has imposed a blockade around Nablus
A gun battle broke out between soldiers and Palestinian militants after tanks and armoured personnel carriers moved into the city and surrounded the Askar refugee camp.
The Israeli military said its forces searched buildings and arrested "about three" Palestinians before withdrawing two hours later.
The army said the operation was aimed at preventing planned attacks by Palestinians against Israelis.
Earlier, a 78-year-old Israeli woman was shot dead and her son wounded after they were ambushed on a road south of Nablus.
Search for militants
Israeli troops, meanwhile, clashed with Palestinian youths in the Palestinian village of Tamoun as soldiers carried out a house-to-house search for suspected Palestinian militants.
The Israeli army said soldiers were looking for accomplices of Palestinian Mohammed Ziad al-Khalili, who attacked the nearby Jewish settlement of Hamra on Wednesday.
An Israeli woman, her disabled 11-year-old daughter and an Israeli soldier were killed in the raid, as well as al-Khalili.
Israeli armoured personnel carriers and tanks first entered Tamoun on Friday.
Military sources said 15 Palestinians were questioned before being released; Palestinian sources said 20 Palestinians were arrested.
The Israeli army said soldiers opened fire after coming under attack by Palestinians throwing stones and explosive devices.
Two Palestinian teenagers were wounded and taken to hospital in Nablus.
'Sanctuary for terrorists'
Israeli troops imposed a blockade on Friday around Tamoun and Nablus, where Israel said al-Khalili came from.
Israel said it was taking action because the Palestinian Authority was failing to stop militants from leaving the city to carry out attacks on Israeli targets.
As the violence continued, European Union foreign ministers meeting in Spain backed a French plan supporting the establishment of a Palestinian state.
French Foreign Minister Hubert Vedrine said the creation of an independent Palestine must be the "starting point of a negotiating process".
The European plan is at odds with the United States' policy, which favours a step-by-step approach to resuming peace talks.