It was the bloodiest violence in Jerusalem since the current wave of unrest began at the start of October and the first time an attack has seen gunfire on a bus.
A 60-year-old was killed and four people wounded in the bus attack in a Jewish neighbourhood of east Jerusalem, while the attackers were also killed, medics and police said.
Media reports said one of the attackers used a gun and the other a knife.
The Jerusalem attacks came after a Palestinian stabbed and wounded a passerby north of Tel Aviv before being detained by civilians in the area.
A wave of stabbings have hit Israel, Jerusalem and the West Bank since October 3.
The attacks along with violent protests in annexed east Jerusalem and the occupied West Bank have led to warnings that a full-scale Palestinian uprising, or third intifada, could erupt.
