Trying to block MPs from leaving the compound, the protesters denounced Abhisit as a frontman for the military, which ousted Thaksin in a 2006 coup.
Al Jazeera's Selina Downes, reporting from Bangkok, said that many remained sceptical as to whether Abhisit would be able to unite the country.
Abhisit would also be under pressure from the growing economic crisis, with Thailand on the brink of recession, she said.
Kasit Piromya, an adviser to the Democrat party, said the new government's priorities would lie first with "reuniting the country" and restoring international confidence in the country."
"[With] the immediate problem of declining prices of commoditities, I think we have to tackled the agricultural sector," he told Al Jazeera.
"And a the same time, we have to look at the labour ... workers will be laid off because of the auto industry cutdown, declining exports, and so on."
The parliamentary vote follows six months of disruptive protests by the People's Alliance for Democracy (PAD), an anti-Thaksin movement, which peaked with a week-long blockade of Bangkok's airports beginning in late November.
The turmoil left 350,000 passengers stranded and has badly damaged Thailand's reputation as a tourist destination and its economy, with GDP growth forecast at just two per cent next year.
The vote makes Abhisit the country's third prime minister in four months after Somchai Wongsawat and Samak Sundaravej – both seen as Thaksin loyalists - were both removed by the courts in what Thaksin supporters called a judicial coup.
Thaksin supporters also claim the military coerced small parties in the previous government to form a Democrat-led government - a claim the army has denied.
Thaksin, who remains in exile abroad to avoid prison after being convicted of corruption, called for national reconciliation on Saturday and urged the military not to meddle in the parliamentary vote.
"May all sides take one step back and respect the results," he said in 20-minute recorded address to 40,000 supporters at a Bangkok sports stadium.
"Please don't use any institution to intervene. Just let the country move forward. Don't make people suffer more."