The move came hours ahead of a deadline set by campaigners for the government to respond to their demands after a massive weekend demonstration.
"They refused to listen to our demands that we gave them 72 hours to fulfil," activist Lucien Bourjeily told AFP.
"They announced clearly that the minister will not resign. We are asking for the resignation of the minister and won't leave until that happens."
The "You Stink" campaign began in response to a trash crisis that erupted with the closure of Lebanon's largest landfill in mid-July.
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Last week, the campaign set out four key demands: the resignation of Environment Minister Mohammed Mashnuq, new parliamentary elections, the devolvement of trash collection to municipalities and accountability for violence against protesters.
The group of protesters sat cross-legged in a hallway outside the minister's office, waving Lebanese flags and chanting "Out, out out! Mashnuq, get out!"
Sit-ins in government buildings are very rare in Lebanon, where public protests are typically called by political leaders.
The group said Saturday after a massive protest that the government had 72 hours to respond to its demands, with that deadline set to expire on Tuesday night.
He said additional measures could yet be announced later Tuesday.
"It will depend on the response of the government."
On its Facebook page, "You Stink" called on supporters "to join us at the Ministry of Environment... To demand the resignation of the minister for failing to solve the trash crisis."
An employee at the ministry, who spoke on condition of anonymity, confirmed that Mashnuq remained in his office, though most of the employees had left.
She said security forces were attempting to negotiate with protesters to convince them to leave the building, which is in downtown Beirut.