Critics say the government's endorsement of the communique undermined Thai claims to disputed territory around the temple.
Ong-art Klampaiboon, the Democrat party spokesman, said signatures of party members were being collected and that an impeachment motion was being drafted.
The opposition has used the long-standing temple issue, which has sparked growing nationalist sentiments, as a weapon against the government of Samak Sundaravej, the prime minister.
Some members of the senate have said they may seek to impeach the entire government which just last month survived a no-confidence motion.
Pressure on government
|Unesco has named Preah Vihear as a World Heritage Site
Also on Tuesday, the Supreme Court ruled against Yongyuth Tiyapairat, a former speaker of the parliament and an executive member of Samak's People's Power party, in a case of electoral fraud that could lead to the dissolution of the People's Power party.
Yongyuth was banned from politics for five years and the Election Commission will now investigate whether his party was involved in the electoral fraud.
It will also forward the case to the Constitutional Court to decide whether to disband it.
Thai election law states that if a senior member of a political party is found guilty of electoral crimes, the entire party could be disbanded if that person is found to have acted on its behalf.
Yongyuth, who resigned from his post as house speaker in February, is a former adviser to Thaksin Shinawatra, the former prime minister who was toppled in a 2006 military coup.
Thaksin has since returned to Thailand from exile to face a slew of court cases over corruption and abuse of power.
Pressure on the government, already reeling from daily street demonstrations, is almost certain to increase because of this week's court rulings and an impeachment motion could prove possible.
But Kuthep Saikrajang, spokesman for the People's Power party, remained confident that the six-party ruling coalition, which commands a majority in parliament, would weather the political storm.
"Even though the government is facing some troubles in legal cases the coalition partners reassure us that they are sticking with the People's Power party," he said.
The street demonstrators, led by the People's Alliance for Democracy, say Samak's government is merely a proxy for Thaksin, an accusation Samak denies.