Thai Prime Minister Somchai Wongsawat has rejected calls by the military to stand down.
Army leader General Anupong Paochinda asked him to call snap elections to end months of political deadlock.
The General also told the protesters to withdraw from the airport and stop the anti-government campaign. However, they continue to do so.
In a television address, Mr Somchai said his government was legitimate and that he would continue to work for the country.
He said the actions of protesters who have occupied Bangkok's main airport and forced its closure were illegal.
Thousands of travellers are stranded in the airport and Bangkok hotels by the closure.
Thailand has been in a state of political stalemate since former Prime Minister Thaksin Shinawatra was ousted in a military coup in 2006.
Fresh elections at the end of 2007 failed to resolve the crisis, when a party made up of former allies of Mr Thaksin returned to power.
Protesters from the People's Alliance for Democracy have been calling on the government to step down since May.