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A report by Jordan's state news agency Petra said Israel sent an official memorandum expressing "deep regret" over the July shooting at Israel's Embassy in Amman and offered compensation to the families of the victims while also agreeing to "follow up" with legal measures.

A statement from Israel's Foreign Ministry said Israel's Embassy will resume full operations immediately. The statement said the shooting incident is being examined and that a conclusion is set to be reached in the coming weeks.

"Israel attaches great importance to its strategic relations with Jordan, and the two countries will act to advance their cooperation and to strengthen the peace treaty between them," the statement from Prime Minister Binyamin Netanyahu said on Thursday.

Israel however has not issued an apology over the killing.

The shooting strained ties between the neighbouring countries which signed a peace agreement in 1994 and cooperate on security and energy issues, among others.

Israel's ambassador went back to Israel along with the guard and other embassy staff after the incident and Jordan subsequently said it would not permit the return of an Israeli ambassador to Amman unless Israel launched legal proceedings against the guard. The guard, who claimed self-defence, had received a hero's welcome in Israel, infuriating the Jordanians.

The easing of tensions came ahead of a visit by Vice President Mike Pence to both countries, starting Sunday.