Dozens of people were killed during the clashes between red shirt protesters and security forces.
Although the impeachment and no confidence motions are unlikely to be passed, the level of support behind them reflects the deep rifts in Thailand's political landscape in the wake of the protests.
Wittaya Buranasiri, the opposition whip, said the motion to impeach Abhisit was introduced by the Pheu Thai Party, which is allied to Thaksin Shinawatra, the former prime minister ousted in a 2006 coup who is widely supported by the red shirt protesters.
Members of the Pheu Thai allege Abhisit and his deputy abused their power in using force in their crackdown on the protests.
The red shirts have been calling for Abhisit to resign and call early elections, arguing his government came to power illegitimately with the help of back-room deals and military pressure.
The demonstrations came to a head when red shirt protesters moved into Bangkok's central business district, building bamboo-and-tire barricades and controlling checkpoints that crippled one of the city's most important shopping and tourism areas.
While shops and businesses have begun to reopen as life in the Thai capital returns to normal after last week's clashes, authorities have said they are considering extending a late night curfew for another week.
"The purpose of the curfew is to separate the terrorists from the public,'' said army spokesman Sansern Kaewkamnerd.
He said the late hours of the curfew would not cause significant disturbances to the public.
The Thai cabinet was expected to meet on Tuesday to approve the extension.