In one deadly incident, members of a Palestinian family were hit by army fire on their balcony, leaving a 19-year-old dead and his father and brother seriously wounded with shots to the head and face, witnesses and medics said.
The Israeli army claims soldiers opened fire after spotting suspicious figures crawling on the roof of a building.
In the second shooting, occupation soldiers opened fire on an 18-year-old on a rooftop. Medics and security sources said the man was standing on the roof of a mosque and had thrown rocks at soldiers below, who then shot him in the stomach and shoulder.
The Israeli army said troops fired at him after spotting him on the roof, fearing he was about to throw a gas canister at them.
Aljazeera's correspondent reports that the city has been sealed off and a curfew has been imposed in certain districts.
The correspondent adds that several relief organisations, such as the International Red Cross Committee, have been refused entry into the old town.
Hundreds of soldiers entered Nablus' old city, or Casbah, on Thursday, and began searching homes and shops. Troops occupied 16 buildings in the Casbah, home to about 20,000 residents and a stronghold of resistance fighters.
Families in the occupied buildings were confined to one room per apartment.
Soldiers forced open doors with grenades and sledge hammers. Palestinian medics said that in all, 12 Palestinians were wounded by live fire.
The military said the Nablus operation, the largest in over a year, would last several days.
The correspondent also reported that the Aljazeera media crew has been prevented from entering the city to report on the situation.