Jordan said on Monday that Israeli President Shimon Peres had apologised to King Abdullah II for the killing of a Jordanian judge by Israeli troops last week.
Peres for his part issued a statement saying he had called Abdullah to express "deep regret" for the shooting of Palestinian Jordanian Raed Zeiter at a border crossing, but the statement stopped short of quoting a full apology.
A Jordan palace statement said Abdullah "received a telephone call from Peres who, as president of the state of Israel, apologised for the martyrdom of Jordanian judge Raed Zeiter".
"Peres expressed his regrets for the incident and said he was deeply affected. He said Israel is committed to work together with Jordan on the probe into the incident."
The statement added the king "also received a similar phone call from (Israeli Prime Minister Benjamin) Netanyahu," without giving further details.
Israeli troops on March 10 shot Zeiter, saying he attacked them, igniting a diplomatic row between Israel and the kingdom and sparking furore among Jordanians.
Israel had previously expressed regret over the shooting, but stopped short of apologising to Jordan, the only Arab country besides Egypt to have made peace with the Jewish state.
The issue ignited a diplomatic row between Israel and the kingdom and caused furore among Jordanians.
- Peres expresses 'deep regret' -
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Peres confirmed he had spoken to Abdullah on Monday, but the wording of his statement left it unclear as to whether he had issued an apology.
"Earlier today I conducted an important conversation with His Majesty King Abdullah II and expressed our deep regret to him," a statement quoted Peres as saying.
"On behalf of the State of Israel, I wish to express my deepest condolences to the people of the Hashemite Kingdom of Jordan for the death of Judge Raed Zeiter at the King Hussein Bridge on March 10."
"As the President of the State of Israel I would like to express compassion to the bereaved family, (and) I share in their grief."
His statement did not mention whether Netanyahu had also spoken to the king.
The Palestinian Centre for Human Rights disputed the army's account, saying one of the soldiers pushed Zeiter after he had disembarked from a bus with other passengers so that Israeli soldiers could search it.
Zeiter responded in kind and other soldiers joined the scuffle, with one of them firing three rounds at his chest, the PCHR said, citing "a witness".
Jordanian Prime Minister Abdullah Nsur has held Israel "completely responsible" for Zeiter's death and demanded an apology for the "hideous" killing.
And MPs have demanded the government expel the Israeli ambassador and release Jordanian soldier Ahmad Dakamseh, who was is serving a life sentence after he opened fire on a group of Israeli schoolgirls in 1997, killing seven.
They gave the government until Tuesday to meet their demands, failing which they threatened a no-confidence vote against Nsur.
Opposition Islamists and other political parties have demanded the 1994 peace deal between Jordan and Israel be annulled.