The victims were named as Amir Banat and Muntassir Hadadi, both aged 15.
Palestinian security and medical sources said the deaths occurred shortly after dark on Saturday after clashes between stone throwers and Israeli soldiers in the dilapidated old sector of Qasaba.
A third Palestinian was seriously wounded by Israeli fire, they said.
The Israeli army has instructions to shoot and kill Palestinian children involved in throwing stones on Israeli troops even if there is no immediate danger to soldiers' lives.
Since the outbreak of the second Palestinian intifada more than four years ago, it is believed that the Israeli army has killed 657 Palestinian minors.
The number of children maimed and injured by Israeli army bullets is believed to be much higher, according to statistics gathered by human-rights organisations, including the Israeli group B'tselem.
During the same period, nearly 130 Israeli children and minors have been killed in Palestinian resistance attacks inside Israel and in the Occupied Territories of the West Bank and Gaza Strip.
The deaths bring to 4580 the total number of people killed since the beginning of the intifada in September 2000, including 3545 Palestinians and 961 Israelis.
"Israeli troops come here almost on a daily basis," Suhair Freitech, external relations' officer at the Nablus governorate, said.
"They shoot in all directions, kill and maim children and other civilians, and then leave. This has become an almost daily routine, even the media has lost interest in these killings because of their frequency."
Other violence in the southern Gaza town of Rafah left four Palestinians wounded by Israeli army fire, according to Palestinian medical sources.
A man in his 60s and two children were among the injured, they said.
On Friday Nablus residents went
to the streets in support of Iraq
Significantly, Karmi Gilon, a former head of Shin Beth, Israel's chief domestic intelligence agency, has admitted that Israeli soldiers are "very much trigger-happy" when dealing with Palestinian civilians.
He pointed out in an interview on Sunday with the Israeli paper Yediot Ahronot that the "assassinations we carry out these days are much less objective and as a result we kill more innocent people knowingly".
In other developments, William Burns, the US assistant secretary of state, will meet PLO chief Mahmud Abbas and other Palestinian leaders on the eve of Secretary of State Colin Powell's visit to the region, an American official said.
Powell is scheduled to meet Israeli and Palestinian officials on Monday.
A Palestinian official said the Palestinian leaders would use the meetings with Burns to set an agenda for contacts with Powell.
The Palestinians have said they want the United States to stick to the Washington-backed road map for peace which sees the establishment of a Palestinian state by the end of 2005.
US President George Bush has now extended that time-frame to 2009 - the end of his second term.
Earlier this month, Bush told a Washington news conference he wanted to see a Palestinian state created before he leaves office.
Aljazeera.net's correspondent in the West Bank, Khalid Amayreh, contributed to this article.