Subhi Saleh, an MP affiliated with the Muslim Brotherhood, Egypt's largest but banned opposition group, said Israeli embassies "in every country" should be stormed if Israelis enter the site.
"Embassies have diplomatic immunity but our holy places have divine immunity, so if they enter Al-Aqsa let us enter their embassies," he said during a heated meeting of his parliamentary bloc.
Tensions over the compound turned violent on September 27 when Palestinians hurled rocks at a group of visitors whom they suspected of being rightwing Jewish extremists.
Home to the Western Wall of the Second Temple, it is Judaism's holiest site and Islam's third most sacred.
Amid the tensions, Israel a week ago denied access to the site to non-Muslim visitors and to Muslim males under the age of 50. But it re-opened the compound on Sunday.
In September 2000, the second Palestinian uprising, or intifada, erupted after Ariel Sharon, a rightwing politician who went on to become Israel's prime minister, visited the site.