Ali al-Abdallah and his son Mohamed have been charged with insulting government employees, Aljazeera said on Tuesday quoting the National Organisation for Human Rights in Syria.
On Monday, rights activists said Syrian authorities had sacked 17 government workers as a punishment for signing a declaration last month that questioned state policy towards Lebanon.
Syria arrested 10 dissidents in May who had signed the Damascus-Beirut declaration, a document urging the Baathist government to mend ties with Lebanon that have been damaged since last year's assassination in Beirut of Rafiq al-Hariri, a former Lebanese prime minister.
One of the 10 who were arrested was among those sacked.
"The regime is showing no leniency, it wants to decimate dissent. The less international pressure on Syria, the more it spreads its totalitarian grip," said Ammar Qurabi, head of the National Organisation for Human Rights.
"These people were fired although they include doctors and engineers in the government for decades."
A government decree sacking the 17 workers was issued on June 14, another Syrian human rights organisation said.
The Damascus-Beirut declaration condemned political killings and called for the establishment of mutual diplomatic ties, which the two countries have never had since their creation in 1920.
It was signed by hundreds of Lebanese and Syrian activists.
Meanwhile, government officials claimed Syria is creating a law to promote multiple political parties in the state.
Syria has faced international calls to democratise a system that allows only 10 parties allied to the ruling Baath party.
Bashar al-Assad, the Syrian president, took power in 2000 and has made repeated pledges of reform, but has maintained the Baath's 43-year monopoly on power.
"We are just about finalising the law for political parties, to be put on the internet for public debate," Buthaina Shaaban, the Syrian expatriates minister told Reuters, on Tuesday.
Shaaban said the presence of more parties did not mean the Baath party would give up its leading role, and added that any new parties would have to "preserve the national unity of the country."