At least two Palestinians were killed by Israel as violence simmered in Jerusalem and occupied West Bank over the weekend.

Palestinian officials said a 23-year-old member of the Palestinian security forces were shot dead in the occupied West Bank on Saturday.

According to Israeli accounts, he allegedly rammed his car into a group of soldiers, wounding three, before being shot dead by another.

In a separate incident overnight another man was killed by Israeli police at the edge of the Al Aqsa Mosque complex in Jerusalem.

The man in question was shot dead after he allegedly grabbed an officer's gun while being detained, the force claimed.

In their reaction, Arab leaders doubted the account while the authorities have opened a probe into the shooting.

The Jerusalem incident at the Al Aqsa Mosque complex, an icon of Palestinian nationalism, came at a high point of Muslim attendance for the holy month of Ramadan amid heightened fears of an escalation in violence.

Israeli-Palestinian tensions are simmering after months of violence in Jerusalem and the occupied West Bank. Friction at Al Aqsa has set off violence in recent years.

However, the sacred site, known to Muslims as the Noble Sanctuary and to Jews as Temple Mount, remained relatively quiet Saturday.

The victim was identified as Mohammad Khaled al-Osaib, 26, a resident of the Bedouin town Hura in south Israel.

Mansour Abbas, a lawmaker whose United Arab List party is popular there, said the man was a medical student, and questioned the police account.

"All we demand is the truth," he said.

The Justice Ministry department for investigating police conduct is looking into the incident, a spokesperson said, adding that the procedure was not a formal investigation.

Asked if the Israeli unit's response was due to misconduct allegations, she said: "There are such claims, and that's why we're looking into it."

Reuters could not immediately verify the police account. Police said the incident occurred at a spot not covered by security cameras. Footage of similar incidents in the past has usually surfaced within a short time.

Police released CCTV footage showing a person they said was al-Osaib walking across the complex alone right before the incident, which a spokesperson said happened in "seconds," and denied reports he had intervened in an altercation with a female worshipper.

Israel's far-right National Security Minister Itamar Ben-Gvir said he backed the officers.