Israeli officials said on Tuesday they would allow a right-wing march in Jerusalem's Old City to go ahead next week under certain conditions, a day after police barred the event's route fearing it would rekindle violence between Israel and Palestinian fighters in Gaza.

Several right-wing Israeli groups had planned a flag-waving procession through the walled Old City's Damascus Gate and into its Muslim quarter on Thursday, drawing warnings from Gaza's rulers Hamas of renewed hostilities should it proceed.

The far-right groups cancelled the Thursday march after police denied them a permit. But following a meeting of Prime Minister Benjamin Netanyahu's cabinet on Tuesday, his office said ministers had agreed the march could be held next week if organisers and police reached an agreement. The principal issue is the route.

“The parade will take place this coming Tuesday (June 15) in a format to be agreed between the police and the parade's organisers,” a statement from Netanyahu's office said.

Netanyahu faces an end to his long hold on power on Sunday when the country's legislature is scheduled to vote on approving a government of diverse parties that came together to unseat him.

If that vote is successful, it will be up to prime minister-hopeful Naftali Bennett and his partner opposition leader Yair Lapid to decide whether to proceed with the march.

Tal Schneider, a leading political reporter in Israel, said on Twitter: “The flag parade has been postponed to June 15, two days after the government is sworn in, meaning it will be Naftali Bennett's headache.”

Tensions are likely to remain high in Jerusalem whether or not the march goes ahead. Protests have flared in the East Jerusalem neighbourhood of Sheikh Jarrah, where Palestinian families face forced eviction after an Israeli court accepted Jewish settler land claims.

Far-right lawmaker Itamar Ben-Gvir rejected the march's postponement as a “surrender to Hamas”, saying on Twitter he would still “arrive on Thursday in the Old City of Jerusalem and march with Israeli flags”.

An original march on May 10 was re-routed at the last minute as tensions in Jerusalem led Hamas to fire rockets towards the holy city. Israel responded with air strikes, and the most serious cross-border fighting with Hamas in years raged for 11 days before a fragile ceasefire was reached.

Israel annexed East Jerusalem, in a move that has not won international recognition, after capturing the area in the 1967 Middle East war. It considers all of Jerusalem its capital.

Palestinians want East Jerusalem to be the capital of a state they seek to establish in the Israeli-occupied West Bank and the Gaza Strip.