One worker was injured in the shooting, which happened near the Jewish settlement of Dugit.
Hours earlier, an Israeli settler and a Palestinian gunman were killed in an exchange of fire at the settlement of Mehora near Nablus in the northern West Bank.
The Mehora violence erupted after the Palestinian Interior Minster, Abdel Razak Yahya, held talks with the head of the US Central Intelligence Agency (CIA), George Tenet, on a new American security plan for the West Bank.
A Palestinian gunman cut through a wire fence to infiltrate the settlement. He killed a woman settler and seriously wounded her husband and another Israeli before being shot dead by troops.
Earlier on Saturday, a Palestinian municipal worker was killed by Israeli soldiers in Nablus.
The army, which has expressed regret over the incident, said that soldiers fired on the 54-year-old man as he was driving through the centre of Nablus.
Nablus has been under Israeli occupation for eight days and a curfew has been in place, but the man had a permit to drive during the curfew.
The army has said that an investigation will take place and disciplinary action taken if soldiers are found to have acted inappropriately.
The Israeli army said it also shot dead a Palestinian who tried to infiltrate Israel from the Gaza Strip with grenades strapped to his body.
CIA plan
Mr Yahya is part of the highest-level Palestinian delegation to visit Washington since President George W Bush called in June for Palestinian leader Yasser Arafat's removal.
Over the past few days, the Americans and Palestinians have been trying to agree on a new security plan.
Correspondents say the idea is that the Palestinian Authority will gradually take over and guarantee security as Israeli forces move back progressively from the West Bank and Gaza.
The CIA would help retrain and reorganise the Palestinian security forces
Israel has insisted that the Palestinian security forces must clamp down on militants before it will pull its forces out of Palestinian towns and cities.
The BBC's State Department correspondent, Jon Leyne, says it is proving very difficult to get an agreement between Israel and the Palestinians on the details of the scheme.
The Palestinians are also complaining that the Americans are dragging their feet.
And our correspondent adds that there is an understandable reluctance by the international community to start rebuilding police stations and other Palestinian institutions that could just end up being blown up once again by the Israelis.