The victim, whose identity was not immediately known, had been shot on Monday evening in a closed military zone around the settlement of Netzarim, just south of Gaza City, hospital sources said.
His body was retrieved on Tuesday by the ambulance service after it received clearance from the Israeli authorities.
It is believed to be the first death of a Palestinian in Gaza at the hands of Israeli troops since President Abbas ordered the large-scale deployment of Palestinian security forces with orders to prevent attacks on Israeli targets.
The teenager's death brings the overall toll since the September 2000 start of the second Palestinian uprising, or intifada, to 4717, including 3662 Palestinians and 981 Israelis.
Abbas has also followed through on his promise to crack down on the resistance by ordering bulldozers to demolish buildings illegally erected on public land and allegedly used to house fighters.
On Tuesday, bulldozers got to work in northern Gaza. Aljazeera reported that tens of heavily armed Palestinian security forces started the demolition work.
Palestinian police clashed with some homeowners and shopkeepers over their properties.
Municipal police official Musa Alian said hundreds of buildings erected without permits would be felled in coming days, adding that their owners had all received advance warnings.
Previous orders to remove the buildings had been ignored in the last years of Yasir Arafat.
"Our Land Authority warned violators once, twice and three times, but the state of chaos that had spread in the community hindered the implementation of the law," he said.
"Our Land Authority warned violators once, twice and three times, but the state of chaos that had spread in the community hindered the implementation of the law"
Musa Alian, police official
"We are now beginning a new era in which law must be respected and all government lands returned."
Thousands of other Palestinian buildings, including homes, have been demolished by the Israeli occupation army in Gaza and the West Bank since 2000, in what it calls efforts to deprive fighters of gun nests and arms-making plants.
Palestinians have denounced such demolitions as collective punishments.