For the second consecutive day, security forces intervened in a bid to break up confrontations late on Monday between the groups' supporters and demonstrators protesting against Lebanon's political elite.
The violence is threatening to tip largely peaceful demonstrations directed at the country's government and its ruling officials in a more bloody direction.
A video posted by Lebanese broadcaster LBCI showed heavy gunfire around Cola bridge in the capital, Beirut. The source of the gunfire was not immediately clear. No injuries were reported. Separately in Beirut, two protesters were reportedly wounded after Hezbollah and Amal supporters attacked demonstrators there.
In the southern town of Tyre, supporters of Hezbollah and Amal tore up protest tents and set them on fire, prompting security forces to intervene and fire into the air, according to Lebanese media.
Lebanon has faced five weeks of anti-government protests, fuelled by anger at corruption among the sectarian politicians who have governed the country for decades. Demonstrators want them all to leave office.
Supporters of Amal and the Iran-backed Hezbollah have occasionally sought to break up the demonstrations and clear roads cut off by protesters. Last month, they destroyed a main protest camp in central Beirut.
The groups were both represented in the coalition government led by Prime Minister Saad Hariri, who resigned on October 29 after the protests began. They had opposed Hariri's resignation.
In a statement, Hariri's Future Movement warned its supporters to refrain from protesting and stay away from large gatherings to "avoid being dragged into any provocation intended to ignite strife".
Groups of men on motorcycles, some waving Amal and Hezbollah flags, were seen roving streets in Beirut and Tyre, according to witnesses and videos broadcast on Lebanese media.
Separately, two people were killed when their car slammed into a traffic barrier on a coastal road on Monday, sparking criticism from Hezbollah and others of protesters who cut off roads as a primary tactic to keep up the pressure.
The confrontations were some of the worst since protests erupted in Lebanon, a country that is facing the worst economic strains since its 1975-1990 civil war.
There are widespread concerns over Lebanon's deteriorating economy and a shortage of US dollars.
Reporting from Beirut, Al Jazeera's Zeina Khodr said that the shortage was "causing a crisis".
"The [Lebanese] economy doesn't rely on the local currency, the lira, importers pay in dollars and many businesses demand payment in the US currency," she said.
The UN Security Council on Monday urged all actors in Lebanon to engage in "intensive national dialogue and to maintain the peaceful character of the protests" by respecting the right to peaceful assembly and protest.
Calling this "a very critical time for Lebanon," the UN's most powerful body also commended Lebanon's armed forces and state security institutions for their role in protecting the right to peaceful assembly and protest.
Overnight Sunday, Hezbollah and Amal supporters attacked demonstrators with stones, tore down protesters' tents and damaged storefronts in the capital, Beirut.
"Shia, Shia, Shia!" Hezbollah supporters waving the group's yellow flag shouted, taunting the protesters, who chanted back, "This is Lebanon, not Iran," and "Terrorist, terrorist, Hezbollah is a terrorist".
At least 10 demonstrators were wounded in the clashes, according to the civil defence.
The consecutive nights of clashes have raised fears that some groups may turn to violence in an attempt to break up the protest movement, while displaying the political and sectarian divisions that protesters say they want to put an end to.
Source: Al Jazeera and agencies