JERUSALEM (Reuters) - Israeli border police shot dead a Palestinian who stabbed them at a police station in the old city of Jerusalem on Monday, police said.

The attacker, armed with a knife, followed two officers in the early morning to a police station near Lions Gate along the old city walls and stabbed both of them, inflicting slight wounds, police spokesman Micky Rosenfeld said.

After a fight, one of the officers shot and killed the attacker, who was from east Jerusalem, he said.

A wave of Palestinian street attacks, including vehicle rammings, shootings and stabbings, began in October 2015 and has slowed but not stopped. Israel blames the violence on incitement by the Palestinian leadership.

The Palestinian Authority, which exercises limited self-rule in the West Bank, denies that and says assailants have acted out of frustration over Israeli occupation of land sought by Palestinians in peace talks that have been stalled since 2014.