Lebanon's top Christian cleric has said it is unacceptable for any party to resort to threats or violence after the worst street bloodshed in the country in more than a decade.
Thursday's shooting, in which seven Shiite people were killed, came amid rising tension over the investigation into last year's port blast.
In his Sunday sermon, Maronite Patriarch Bechara Boutros Al Rai said “no one is above the law and judiciary”.
Thursday's incident in Beirut marked the second deadly sectarian clash in five months. Violence in June took the lives of at least four in Khalde, south of Beirut.
Mr Rai said “we must free the judiciary from political interference” and “sectarian and partisan political activism".
Lebanon's council of ministers must meet, take decisions and respect authority, he said.
The Iran-backed Shiite Hezbollah group opposes the investigation and has called for the lead investigator into the blast, Judge Tarek Bitar, to be removed. Mr Bitar's predecessor, Fadi Sawan, was removed because of political pressure after indictment of two former ministers.
Global leaders expressed concern over Thursday's violence and called for an investigation. Leaders also called for the continuation of the investigation into the Beirut port blast, which killed at least 214 people.
UN Secretary General Antonio Guterres called for an immediate end to the violence and stressed the need for an impartial investigation into the blast.
A Lebanese Hezbollah MP said on Sunday that the shooting at the protesters amounted to a “massacre” and its perpetrators should be held to account, the state-run National News Agency reported.
“What the criminals … did is a massacre and it will have important ramifications,” MP Hassan Fadallah said. “Those who incited, planned … and opened fire should be held to account all the way up to the top.”
Hezbollah had accused members of the Lebanese Forces, the country’s second biggest Christian party, of firing at demonstrators.
Mr Fadlalah said the shooting was aimed at luring the party into a domestic conflict, accusing the Lebanese Forces of serving foreign agendas.
The party's leader, Samir Geagea, has accused Hezbollah of storming peaceful neighbourhoods and vandalising property, which he said prompted local residents to clash with Hezbollah loyalists and their Shiite allies in Amal, the movement led by the parliament speaker.
Mr Geagea said Hezbollah's move was reminiscent of the May 7, 2008 events when the Iran-backed group's gunmen overran parts of Beirut.
Gebran Bassil, the leader of the Free Patriotic Movement — the largest Christian party and the group founded by President Michel Aoun — accused Mr Geagea of inciting strife.
Mr Bassil, the target of US-corruption related charges, is a staunch ally of Hezbollah and a presidential aspirant.