"The Israeli lawmaker entered the compound under Israeli police protection and accompanied by television crews," guard Naser Qous told Anadolu Agency.
"Feiglin stood up at the Dome of the Rock Mosque and demanded that Palestinians be deported," Qous added.
Feglin was quoted by the Palestinian Wafa news agency as saying from inside the compound that the site was "for the Jewish people."
Palestinians, he reportedly added, "should be deported to Saudi Arabia, where they have their own place to pray."
"The Dome of the Rock is a Jewish temple, not a Muslim mosque," the lawmaker asserted, according to the news agency.
Feiglin recently called for holding a special session of the Knesset (Israel's parliament) devoted to discussing proposals for the imposition of Israeli "sovereignty" over Al-Aqsa, Islam's third holiest site – but the session was later cancelled.
Since the 1950s, all Muslim and Christian religious sites in Jerusalem's Old City have been administered by neighboring Jordan.
A 1994 peace treaty between Israel and the Hashemite Kingdom recognizes the latter's special supervisory role over holy sites in the historical city.
Al-Quds was captured by Israel during the 1967 Middle East war. In 1980, Tel Aviv annexed the city in a move never recognized by the international community.
Jews refer to the Al-Aqsa Mosque complex as the "Temple Mount," claiming it was the site of two prominent Jewish temples in ancient times.
In September 2000, a visit to the site by controversial Israeli politician Ariel Sharon sparked what later became known as the "Second Intifada" – a popular uprising against the Israeli occupation in which thousands of Palestinians were killed and injured.