Sweden, Egypt and France requested the meeting to "urgently discuss how calls for de-escalation in Beit ul-Muqadass can be supported", Carl Skau, Sweden's deputy United Nations ambassador, said on Twitter.
Palestinian President Mahmoud Abbas, meanwhile, announced that he is freezing ties with Israel, dealing a blow to fledgling Trump administration efforts to try to renew long-dormant peace talks.
A Palestinian man runs in front of an Israeli military machinery during clashes with Israeli troops in the West Bank village of Khobar near Ramallah July 22, 2017.
On Friday, Egypt called on Israel to immediately stop its violent actions and cancel its escalated security measures against Palestinians in Jerusalem and the Al-Aqsa Mosque area, expressing "deep concern".
Two Palestinians died in clashes with Israeli forces on Saturday as the army moved in to seal off an attacker's home, following violence over security measures at an ultra-sensitive holy site.
However, the compound was reopened on July 16, but with metal detectors and surveillance cameras put up at entrances.
Palestinian U.N. envoy Riyad Mansour told reporters: "We are against violence. and we want the Security Council to have the political will to protect the Palestinian people against such violence from the Israeli occupying authority".
Israel installed metal detectors at the entrance of a holy site, prompting an outcry from Muslim worshipers and an uptick in violence.
Some Israeli ministers have suggested that the 19-year-old assailant responsible for Friday's knife attack should receive the death penalty, a sentencing option that remains available in Israel's military courts but has not been used since 1962.
Hezbollah flags were waved and Israeli flags were burned outside Israel's London embassy this weekend as scores of demonstrators vented their anger at new security measures at Temple Mount in Jerusalem. The three alleged Palestinian perpetrators were tracked to the Al-Aqsa where they were shot and killed by Israel police.
The Palestinians, as well as some Arab countries, urged Israel to remove the gates, saying it was a violation of the long-held status quo under which the Muslim Waqf is in charge of running the site.