AMMAN (Reuters) -A gunman was dead and three policemen injured after a shooting near the Israeli embassy in neighbouring Jordan, a security source and state media said on Sunday.

Police shot a gunman who had fired at a police patrol in the Rabiah neighbourhood of Amman, state news agency Petra reported, citing public security, adding investigations were ongoing.

Jordanian police had earlier cordoned off an area near the heavily policed embassy after gunshots were heard, witnesses said. Two witnesses said police and ambulances rushed to the Rabiah neighbourhood, where the embassy is located.

The area is a flashpoint for frequent demonstrations against Israel. The kingdom has witnessed some of the biggest peaceful rallies across the region as anti-Israel sentiment runs high over the war in Gaza.

Police had called on residents to stay in their homes as security personnel searched for the culprits, a security source said.

Many of Jordan’s 12 million citizens are of Palestinian origin, they or their parents having been expelled or fled to Jordan in the fighting that accompanied the creation of Israel in 1948. Many have family ties on the Israeli side of the Jordan River.

Jordan's peace treaty with Israel is unpopular among many citizens who see normalisation of relations as betraying the rights of their Palestinian compatriots.

(Reporting by Suleiman Al-Khalidi and Jaidaa Taha; Editing by Chizu Nomiyama)