Palestinian media reports said Hatem Shadid, from the West Bank village of Alar, was killed after his car collided with an Israeli Jeep.
Shin Bet, the Israeli security agency, said Shadid purposely rammed his vehicle into the Jeep, causing it to overturn, slightly injuring its four occupants.
Shadid then got out of his vehicle wielding an ax and headed toward the agents shouting, "Allahu akbar (God is great)," officials said.
He injured one of them before he was shot, Maariv reported.
Gershon Masika, head of the Samaria regional council, praised the agents' actions.
"The government should learn from the security agents' determination in combating terror. A terrorist tried to attack Jews and the only action required is to destroy him," he said.