A Palestinian stabbed an Israeli border policeman outside Jerusalem's Old City on Sunday, critically wounding him, with the officer managing to shoot his attacker, leaving him in critical condition.

Police described the incident, which took place just outside Damascus Gate, as a "suspected terror attack," saying the attacker was an 18-year-old Palestinian from the West Bank.

"An 18-year-old resident of the West Bank stabbed a border police officer in the neck with a knife, and the border police officer was taken in critical condition to Shaarei Tzedek hospital in Ein Kerem," police spokeswoman Luba Samri said in a statement.

"The border police officer managed to fire at the terrorist, critically wounding him," she said.

The attack took place two days after a Palestinian shot dead an Israeli hiker near the West Bank city of Ramallah as Palestinians marked the first Friday of the Muslim fasting month of Ramadan.