While UN Secretary-General Antonio Guterres on Tuesday closely followed one of the greatest surges of violence in the Gaza Strip in years, his spokesman said a UN special coordinator is "making headway" in attempts to stem the violence.

"The Secretary-General is following closely the latest security developments in Gaza," said Farhan Haq, deputy spokesman for the UN chief. "He urges all parties to exercise maximum restraint."

"The United Nations Special Coordinator Nickolay Mladenov is working closely with Egypt and all concerned parties to restore calm," Haq told reporters at a regular briefing.

The United Nations has been "making progress ... in Gaza with respect to the work that Nickolay Mladenov is doing with regard to the parties and the assistance of Egypt," Haq said.

There was at least one published report the Palestinians agreed to a cease-fire as long as the Israelis honored it. It reportedly was brokered by Egypt. However, there was no immediate confirmation of the report from the world organization or other actors in the crisis.

The United Nations "is working closely with Egypt and all concerned to ensure that Gaza steps back from the brink," Mladenov tweeted on Monday. "The escalation in the past 24hrs is EXTREMELY dangerous and reckless. Rockets must STOP, restraint must be shown by all! No effort must be spared to reverse the spiral of violence."

Later on Tuesday, the Palestinian representative to the United Nations, Riyad Mansour, sent identical letters to the secretary-general and heads of the Security Council and the General Assembly, protesting an Israeli raid that touched off the latest round of violence.

Mansour's letter said that since Monday Israel has been carrying out large-scale assaults against civilian areas in the Gaza Strip. These air strikes constitute the most intense military raids and attacks since 2014.

Almost immediately afterward, Israel's representative, Danny Danon, met reporters outside the Security Council chambers to protest a barrage of rockets fired on Israeli territory.

He said more than 400 rockets had been fired by Hamas from the Gaza Strip into southern Israel and then played from his mobile phone a recording of a wailing air raid siren, saying families had "15 seconds to find shelter" after the alarm sounded.