Jordan's King Abdullah told Israeli Defence Minister Benny Gantz in Amman on Tuesday that Israel must refrain from provoking Muslims in Jerusalem during Ramadan.
The monarch has been on a diplomatic drive in the past week to cool down escalating tensions in Jerusalem.
In May last year, confrontations between Israeli right-wing nationalists, local Palestinians and Hamas supporters drew a police crackdown.
Tensions culminated in a devastating 11-day war between Israel and Hamas that left at least 256 Palestinians dead in Gaza and killed 12 people in Israel, including citizens of other countries.
King Abdullah will meet Israeli President Isaac Herzog in Jordan on Wednesday, the two governments said.
Jordanian state media quoted the king as telling Mr Gantz that preserving calm during Ramadan requires guaranteeing freedom of worship at Al Aqsa Mosque, one of Islam's holiest sites, and "preventing provocations that could lead to escalation".
Ramadan is expected to start at the weekend.
Jordan has sought to raise its regional profile since the election of US President Joe Biden in November 2020, after years of disagreement between Jordanian officials and the Donald Trump administration.
Mr Trump was seen by Amman as having attempted to sideline the kingdom, particularly in regard to the Palestinian issue, as Washington prioritised normalisation of Arab states with Israel.
The kingdom considers itself as having a special status in relation to Al Aqsa Mosque, dating from the early 20th century, when religious leaders in Palestine awarded the Sharif of Makkah, the great grandfather of King Abdullah, custodianship of the shrine.
The 1994 peace treaty between Jordan and Israel says that Israel "respects the present special role" of Jordan in "Muslim Holy shrines in Jerusalem" and recognises "the Jordanian historic role in these shrines."
The last war between Hamas and Israel in May erupted partly because of an Israeli raid on Al Aqsa at the beginning of Ramadan.
A large proportion of Jordan's 10 million people are of Palestinian origin.
Jordanian officials regard Israeli actions in recent years against the Palestinians as increased repression that could result in another mass movement of Palestinians into the kingdom, similar to the two refugee waves in 1948 and 1967.
The king told Mr Gantz that "all measures that undermine peace must be stopped", and that Palestinian-Israeli peace can only be achieved on the basis of a two-state solution.
Although Jordan has been intensifying contacts with Israel, it was not part of a meeting in Negev, Israel this week between senior ministers from the UAE, Israel, Bahrain, Morocco, Egypt and the US.
Israeli Foreign Minister Yair Lapid said the Negev meeting aimed at building up regional deterrence against Iran.
The meeting took place amid expectations of a deal between the US and Iran to return to a nuclear accord abandoned under President Trump.
A senior Jordanian official said on condition of anonymity that Jordan was invited to the meeting but chose not to attend.
An official Israeli statement said President Herzog will be making a "historic public presidential visit" to Jordan on Wednesday, and indicated that ways to reduce tension in the holy land in Ramadan will be on the agenda.
"The two leaders will discuss several issues, including deepening Israeli-Jordanian relations, maintaining regional stability with an emphasis on the coming holiday period," the statement said.