The Izz al-Din al-Qassam Brigades - the military wing of Hamas - sent a statement to Aljazeera on Thursday confirming that Muhannad al-Lahham was shot after infiltrating the Ganei Tal colony and attacking a group of Israeli soldiers.
An army spokeswoman said the fighter had opened fire on a patrol and thrown grenades. She did not comment on any military casualties.
The attack comes as a far-right member of Jerusalem's Israeli municipal council vowed to sabotage the Palestinian presidential election in the city's Arab sector by blocking access to the polling stations.
David Adari told Israeli army radio that "there will be several hundred of us coming to pay bills, buy stamps and thus create long queues inside and outside the post offices" where the polling is to take place.
Preventing a vote
Adari, a member of the pro-settler National Religious Party, said the aim of the operation was to delay the voting and dissuade East Jerusalem Palestinians from taking part in Sunday's election.
Army radio said several Arab Israeli members of parliament made a plea to Prime Minister Ariel Sharon, asking him to prevent the sabotage attempt.
Some members of the Israeli government had been reluctant to allow the residents of East Jerusalem to take part in the election for fear that it would undermine negotiations towards a final status agreement.
However, Sharon agreed after international pressure, to allow voting via post offices in a repeat of the procedure used in the last election in 1996.