Israeli army officials said the Palestinian who activated the explosive was killed by troops, as was another Palestinian fighter who they said had opened fire on soldiers.
The Islamic Jihad organisation claimed responsibility for the attack.
The killings highlighted the challenges Mr Abbas faces in his effort to end the intifada, now in its fifth year. During his campaign, he said that armed attacks harm the Palestinian cause and that he would seek to persuade Islamic Jihad, Hamas and other groups to stop them, thereby putting the onus for peacemaking on Israel.
In the West Bank, meanwhile, army and Shin Bet forces killed two gunmen when they came under fire as they entered Qarawat Banizeid, near Ramallah.