"My position is not important. But democratic values are," he said.
Gen. Anupong Paochinda, chief of the army, had earlier called a meeting with high-level government officials, academics, economists and security officials.
"The government should give the public a chance to decide in a fresh election," Anupong said at a news conference after the meeting.
A spokesman for the protesters also rejected the army chief's solution, saying that new elections alone would not end the standoff, calling for Somchai to resign unconditionally. He added that the group would not leave the airport, where thousands of travelers are stranded.
The bold takeover, which comes at the height of Thailand's tourism season, threatens to further strain the industry, already reeling from months of political unrest and the global financial downturn. Tourism makes up 6 percent of the economy, which grew at its slowest rate in more three years in the last quarter.
All flights were canceled and frustrated passengers bused to hotels, as protesters shut down Suvarnabhumi Airport in a major escalation of their four-month campaign to oust Somchai.
The protest group, the People's Alliance for Democracy, known as the PAD, appears intent on forcing the military to intervene and bring down the elected regime.
"We sympathize with the passengers but this is a necessary move to save the nation," top protest leader Sondhi Limthongkul said on a makeshift stage at the besieged airport amid resounding applause. "If he doesn't resign, I will not leave."
Suriyasai Katasila, a spokesman for the alliance, said later after a meeting of the alliance's leaders that the group would also continue to hold the other two locations they have overrun: the prime minister's office compound and another airport.
He added: "Dissolving the Parliament does not solve the problem.... We do not want Somchai's government, even as acting government before a fresh election is called."
By late afternoon, most of the 4,000 travelers, some who had been camped out since the night before, had left, a Thai tourism official said.
That left the protesters, a sea of matching yellow shirts, and they appeared to be settling in for the long haul.
They spread blankets on the floor, used luggage trolleys to carry boxes of water around the sprawling terminal and set up stands selling food and the plastic hand-clappers they use at rallies.
There was no word on when flights might resume. The U.S. Embassy advised Americans to stay away from the airport, while the Philippines and Singapore recommended that nonessential travel to Thailand be canceled.
Tempers frayed at sprawling Suvarnabhumi Airport, a major hub in Asia that averages 700 flights a day.
"I understand nothing, nothing, nothing," said French tourist Denis Hapard. "We don't understand what's happening. We're really upset."
Among those stranded were Americans trying to get home for the Thanksgiving holiday on Thursday.
Cheryl Turner, 63, of Scottsdale, Arizona, had asked neighbors to pull an 18-pound turkey from her freezer a day ahead of time to defrost so she could cook it for a traditional Thanksgiving dinner.
"My turkey is sitting in the sink at home," she said.
Protesters distributed flyers trying to explain their action.
After reading the flyer, Clay Judd, 30, of Jackson Hole, Wyoming, said he didn't know what to make of the situation.
"For us to be upset because we can't have a huge turkey dinner - so what?" Judd said, waiting in a crowd inside the terminal to get bused to a hotel.
Support for the protesters has been waning, and the group appears to be edging toward bigger confrontations - involving fewer though more aggressive followers - to challenge the government.
Early Wednesday, assailants threw four explosives at anti-government demonstrators, including one targeting a group about a half-mile (one kilometer) from the airport.
A second was tossed into a crowd of anti-government supporters gathered at the domestic Don Muang airport, injuring three others, police said. Two other explosives were thrown in Bangkok, but no one was injured. It is unclear who staged the attacks.
The airport blockade - carried out while the prime minister was abroad - is a fresh blow to Thailand's $16 billion-a-year tourism industry.
Airport director Serirat Prasutanont, who had tried to negotiate with the protesters to allow passengers to fly out, said the takeover "damaged Thailand's reputation and its economy beyond repair."
The airport, the 18th-busiest in the world, handled over 40 million passengers in 2007.
"We don't have an estimate of financial loss, but it is greatly damaging," said Vijit Naranong, honorary chairman of Tourism Council of Thailand.
Demonstrators swarmed the international airport overnight, breaking through police lines and spilling into the passenger terminal.
Group Capt. Chokchai Saranon, a control tower official, said 50 masked protesters armed with metal rods demanded to enter the control tower Wednesday, seeking the prime minister's flight schedule. Three were allowed in, but with flights canceled, there were no controllers to provide the information and the protesters eventually left.
The People's Alliance for Democracy has been trying to topple Somchai, accusing him of being the puppet of a predecessor, billionaire Thaksin Shinawatra, who was convicted of corruption and other charges. The alliance said protesters would keep the airport closed until Somchai quits.
The alliance has staged a number of dramatic actions in recent months. It took over the prime minister's office in late August and twice blockaded Parliament - one time setting off street battles with police that left two people dead and hundreds injured.
