The Puea Thai party is aligned to Thaksin Shinawatra, the former prime minister who was removed in a 2006 military coup.
"I'm not afraid of any knockout punch, as I haven't committed any shameful acts"
Abhisit Vejjajiva, Thai PM
Aside from the prime minister, Korn Chatikavanij, the finance minister, his deputy Pradit Patharaprasit, Kasit Piromya, the foreign minister, Chavarat Charnvirakul, the interior minister and his deputy Boonchong Wongtrairat were also named in the motion.
Abhisit, a British-educated economist who, came to power in December following months of political unrest and street protests, said he was confident his administration would be able to ride out the threat.
"I'm not afraid of any knockout punch, as I haven't committed any shameful acts," Abhisit told reporters in Bangkok before heading to parliament for the two-day debate.
"I am not excited at all, because I have been in parliament for a long time and the process is normal in democratic rule."
Part of the debate is expected to focus on links between the Abhisit's Democrat Party and protesters who occupied the prime minister's office and Bangkok's two airports last year in a bid to unseat a previous pro-Thaksin government.
In launching the debate on Thursday, Chalerm Yoobamrung, the chairman of the Puea Thai party MPs, accused Abhisit of certifying false party financial statements for 2004 in his capacity as leader.
He also alleged that the Democrat Party had received illegal donations worth more than $5.7m from its members.
"Abhisit has gravely violated political party law twice," Chalerm told legislators.
Resignation is customary if a majority of lawmakers vote against any minister, but the Democrat-led ruling coalition controls a majority in the house and is expected to prevail.
Earlier on Thursday Abhisit said a recent string of attempted bomb attacks in southern Thailand were an attempt by critics to destabilise his government.
Police Colonel Pornsak Nuannoo said officers defused four small explosive devices in Surat Thani province, a stronghold of Abhisit's party.
Abhisit said the bombs represented "a hidden political agenda" and "an attempt to discredit the government".