The families moved a few kilometers outside of town, where they said they would encamp on an empty plot of land.
The petition, which was launched Thursday, calls for the courts to drop the charges against the detainees and release them without conditions.
Nine people were injured, three of them seriously, when housing rights demonstrators clashed with police on Friday morning.
At least four people were killed and dozens injured when police opened fire on protesters Jan. 3.
Reporters Without Borders has put Cambodia on a list of countries in a “difficult situation” in its annual Press Freedom Index.
Cambodia ranks No. 144 of 180 countries on the index, above China, Iran, Vietnam, Sudan and others.
The Cambodian Court of Appeals has denied bail to 21 detained labor protesters, setting the stage for more demonstrations on their behalf.
The 21 detainees were among 23 arrested in deadly labor protest crackdowns in January.
21 defendants charged with intentional violence and destruction of property during garment factory workers strike in Phnom Penh on January 3.
A confederation of 16 labor unions says it will hold another mass protest if the government refuses to release 21 detained labor activists.
The leaders from 16 unions met Monday to decide what to do after two of 23 workers were released from custody on Friday.
Riot police and security forces barred an opposition delegation from meeting with 23 protest detainees in Kampong Cham province.