Hezbollah later issued a statement saying it supported peaceful protests against "endemic corruption," calling it a legitimate right. The statement suggested the powerful group was throwing its weight behind the protest movement now calling on the government to resign.
Prime Minister Tammam Salam had called for the emergency meeting after a weekend of clashes between security forces and demonstrators protesting against corruption and poor public services.
The six ministers withdrew four hours into the meeting. Foreign Minister Gibran Bassil, whose Free Patriotic Movement is aligned with Hezbollah, said he was pulling out because of a "theater" being performed with regards to the trash issue.
The trash crisis has emphasized the long-existing fault lines in Lebanon which in recent years has pitted the Iran-backed Hezbollah group against the country's Western-backed, pro-Saudi camp.
The Cabinet also unanimously rejected the winning bidders to manage Beirut's trash announced by the environment minister a day earlier, citing high costs. The Cabinet tasked a ministerial committee with restarting the bidding process, suggesting there was no imminent solution for the crisis that has sparked the protests.
Anger about the heaps of trash accumulating in Beirut's streets boiled over this week with thousands protesting the government's failure to deliver basic services. The clashes turned violent over the weekend, prompting the government to erect a concrete wall outside its main building to prevent protesters from reaching it.
Struggling to contain street anger, authorities began removed the wall Tuesday, 24 hours after it was installed.
The wall was being taken down on orders from Salam, likely as a move to appease demonstrators who dubbed it a "wall of shame."
Lebanon's multi-sectarian power-sharing government has been without a president for more than a year, and parliament has extended its term twice without elections.
Meanwhile, intense clashes persisted Tuesday in the largest Palestinian refugee camp in Lebanon between Islamists and members of the Palestinian Fatah movement, killing three people and forcing hundreds to flee, Palestinian security officials said.
The fighting, which began Saturday in the Ein el-Hilweh refugee camp near the southern port city of Sidon, followed a failed assassination attempt targeting a Fatah party official. Fatah is the party of Palestinian President Mahmoud Abbas. Three people were already killed in the clashes on Saturday.
The clashes involved rockets and heavy machine gunfire, causing serious damages to homes, and wounding at least 20, the security officials said, speaking on condition of anonymity because they were not authorized to speak to journalists.
They said a cease-fire was reached later Tuesday.