Israel's Prime Minister Benjamin Netanyahu spoke Thursday by telephone to King Abdullah II, the premier's office said, apparently their first contact since Jordan announced its ambassador was returning to Tel Aviv.

"Prime Minister Netanyahu extended his condolences to the King and to the Jordanian people" over the murder of a Jordanian air force pilot by the Islamic State group, a statement said.

Netanyahu "noted the importance of the Jordanian ambassador's return to Israel and of the joint commitment to maintaining the status quo at the holy sites" in east Jerusalem, it said.

On Monday, Amman announced that its envoy would return to his post in Tel Aviv three months after being recalled over "violations" at Jerusalem's al-Aqsa mosque.

Jordan recalled Walid Obeidat on November 5 after police clashed with stone-throwing Palestinians inside the flashpoint al-Aqsa compound, with Foreign Minister Nasser Judeh describing Israeli actions as "violations" and "way beyond the limits".

Jordan said the decision to return Obeidat to Israel comes after the government "felt that the situation (at al-Aqsa) is in the right direction".

Obeidat's recall had put enormous pressure on already frosty ties between Israel and the only Arab country apart from Egypt to have signed a peace treaty with the Jewish state.

Tensions soared to new heights when in early November Israeli police entered several meters (yards) inside al-Aqsa mosque during clashes triggered by a vow by Jewish far-right groups to visit the holy site.

The compound, holy to both Muslims and Jews, is one of the most sensitive spots in the Middle East.

Jordan, where almost half the population of seven million is of Palestinian origin, has historical custodianship over the flashpoint site and other Muslim holy sites in Jerusalem.