Israeli right-wing groups Monday cancelled plans for a controversial march through annexed east Jerusalem this week, citing police restrictions, as Islamist group Hamas warned the event would spark new violence.

The so-called March of the Flags was due to take place on Thursday and proceed through flashpoint areas of east Jerusalem that have seen repeated clashes recently between Israeli police and Palestinians.

"Police refused to give us authorisation" for the requested route, a spokesperson for one of the groups organising the march said.

Israeli police said in a statement that "the current route at this time is not approved", without stating that the march had been scrapped.

But some extreme-right Israeli politicians said they would go ahead with the march anyway.

Ultra-right wing MP Itamar Ben-Gvir, whom police have accused of stirring unrest in Jerusalem, along with conservative Likud member May Golan tweeted that they would march in Jerusalem on Thursday, which they can do with parliamentary status.

The statement from police came as Khalil Hayya, a senior figure of the Palestinian group Hamas ruling Gaza, warned the march could spark new violence, following the military escalation of May 10-21.

"We warn the occupation (Israel) against letting the march approach east Jerusalem and Al-Aqsa Mosque compound on Thursday," Hayya said. 

"We hope the message is clear so that Thursday doesn't become (a new) May 10."

The latest war started after Hamas had issued a short deadline for Israel to remove its security forces from flashpoint areas in east Jerusalem, then launched its first volley of rockets at Israel.

Earlier on May 10, organisers had called off plans for another march, to mark "Jerusalem Day". The event commemorates what Israelis consider the "reunification" of the disputed city following the 1967 Six-Day War, when it seized east Jerusalem before annexing it.

Right-wing organisers have described this week's planned march as a routine demonstration of free expression, but many critics feared it could set a match to already inflamed tensions.

The march was set to pass through the Old City's Damascus Gate, the site of clashes last month between anti-settlement demonstrators and Israeli security forces.

Defence Minister Benny Gantz had urged police to cancel Thursday's event over concerns it could reignite fighting.

In the latest Gaza war, Israeli strikes killed 260 Palestinians, including 66 children and some fighters, and wounded over 1,900 people, the Gaza health ministry says.

Rockets and other fire from Gaza killed 13 people in Israel, including a child and an Arab-Israeli teenager and an Israeli soldier, medics and the military say. Some 357 people in Israel were wounded.