Some marchers carried black versions of the Lebanese flag in a sign of mourning for the more than 190 people who were killed in the August 4 explosion at the Beirut port, and others demanded the president resign.
Twenty-five suspects are in custody over the tragedy that occurred when hundreds of tonnes of ammonium nitrate fertiliser that had been left unattended in a port warehouse exploded.
The blast, which wounded thousands and destroyed homes and businesses across large parts of Beirut, was one of the biggest non-nuclear explosions ever.
The government resigned in the wake of the disaster, but Lebanon has rejected an international investigation, saying it would carry out its own probe aided by foreign experts.
Saturday's march set off from the justice palace in Beirut to the hillside presidential palace, where there were also hundreds of supporters of President Michel Aoun and heavy army deployment.
Troops fired warning shots into the air as brawls between rival demonstrators broke out, AFP correspondents said.
"It is not possible that no one has been put on trial after an explosion like the one that happened on August 4," anti-government protester Layal Tohme said.
"The country is collapsing," she added.
Darine Hourani, a supporter of Aoun, said the president "cannot be held to account each time something wrong takes place" in the country.
"He is the president and we must respect him," Hourani added.
But Carla Moukahal, a critic of Aoun, said the president must step down.
"I came here to bring down this corrupt political system. We want to oust Michel Aoun. Enough is enough," said the 19-year-old.
The army said in a tweet that it had formed a cordon to separate the rival protests and that soldiers "fired into the air after some demonstrators pelted soldiers with stones and beat them with sticks".
A protest movement that erupted in October last year has been revived since the blast, which rekindled smouldering rage against official neglect and a political class accused of corruption.
The explosion, Lebanon's worst peace-time disaster, was followed by a fire on Thursday at the Beirut port, and came as Lebanese were already reeling from the country's worst economic crisis in decades.
Among those arrested by authorities as part of the investigation into the blast are top port and customs officials, as well as Syrian workers who allegedly carried out welding work at the port hours before the explosion.
No high-ranking political official has been arrested as part of the probe.
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