An Israeli general has apologised to Jordanian King Abdullah for saying he might be the last of the Hashemite dynasty to rule Jordan.
Gen Naveh said Islamists were a threat to the monarchy
Jordan insisted Maj Gen Yair Naveh be reprimanded after he said the king risked being toppled by an "Islamist axis" stretching from Iran to Gaza.
The Israeli government has distanced itself from Gen Naveh's comments.
The Hashemites have ruled since the king's great-grandfather, Abdullah I, became Emir of Trans-Jordan in 1921.
Gen Naveh, the head of the Israeli army's Central Command, sent a letter of apology to his Jordanian counterpart on Thursday morning.
In his letter, he said he was sorry "if my comments upset the Jordanian people and King Abdullah II", Israeli army radio reported.
Speaking at a lecture to journalists and diplomats at the Jerusalem Centre for Public Affairs on Wednesday, Gen Naveh said an "Islamist axis" was threatening to envelop Jordan.
He said the axis comprised Iran, "which proclaims its desire to destroy Israel", Iraq, "where no one knows what might happen", and the Palestinian territories, where the Palestinian Islamist militant group, Hamas, won last month's legislative elections.
"Given that Jordan is 80% Palestinian, we might - heaven forbid - reach a situation in which Abdullah is the last Hashemite king," he said.
Jordan has a large population of citizens of Palestinian origin who left homes in what is now Israel and the occupied territories, although few observers put the percentage as high as Gen Naveh.
The Jordanian charge d'affaires in Israel, Omar al-Nadif, criticised Gen Naveh's prediction, warning the remarks would harm relations between Jordan and Israel if "appropriate action" was not taken.
Israeli Defence Minister Shaul Mofaz and Israeli army Chief of Staff Dan Halutz have issued a joint statement stressing the comments did not reflect Israel's position and demanding an immediate inquiry into the issue.
"Israel views Jordan as a strong, stable country, with a glorious heritage and promising future," it said.
"Israel wishes to express respect and appreciation for the Hashemite Kingdom's vital contribution to regional stability and peace."
It is not clear if the statement has placated Amman. Correspondents say the Jordanians want Gen Naveh's resignation.
In addition, Gen Naveh said a Hamas-led Palestinian Authority risked becoming an "enemy state".
"One should understand very clearly what the leaders of Hamas say and take them seriously. They have every intention of throwing us into the sea, doing it step by step and getting others to do their dirty work for them."