Moscow has voiced "deep concern" after the recent tension between Israel and Palestine, the Russian Foreign Ministry said on Monday.
"We call on both sides to show restraint so as to be able to prevent the violence from escalating Palestinian-Israeli tension," the ministry said in a statement.
It said Russia believed there was no justification for "extremism" no matter what reason was provided.
Anger has spilled across the West Bank since last week when Israel shut East Jerusalem’s Al-Aqsa Mosque, venerated by Muslims and Jews -- who call the site Temple Mount -- following a deadly shootout.
The mosque was reopened after two days, with Israel installing metal detectors and cameras at its gates. Palestinians say this aims to change the status quo -- a delicate balance of prayer and visiting rights.
Israel refused to remove the detectors, claiming the security measures were similar to procedures taken at other holy sites around the world.
Three Palestinians were killed on Friday in protests against the Israeli measures around the holy site. Three Jewish settlers were also killed in an alleged Palestinian attack in a settlement in the West Bank.
The city of Jerusalem is sacred to members of all three Abrahamic faiths -- Muslims, Jews and Christians -- and the Al-Aqsa Mosque represents the Islamic world's third-holiest site.
"There must be free access to the holy places in East Jerusalem, which are of crucial significance to the believers of three monotheistic religions [...]," the Russian Foreign Ministry said.
It also said Russia was "resolved" to continue to promote lasting peace between Palestinians and Israelis.