Baledogle is the biggest military airport in Somalia, about 100km west of Mogadishu.
Ali Mohamed Gedi, speaking late on Sunday from his base in Baidoa, said: "My confidence is very high. We have enough military forces to defeat any invasion, any attack by the terrorists of the so-called Islamic courts."
The prime minister said that the Islamic courts forces had 8,000 foreign fighters in their ranks and, on Monday, a government spokesman said that Somalia had closed its borders.
"The government has decided to close our borders, air space and sea space," Abdirahman Dinari said. "We are requesting the international community, especially neighbouring states, to help us effect this."
Gedi said that his government, backed by the Ethiopian military, would be victorious. He said that government troops inflicted a serious defeat on the fighters near the town of Dinsoor on Sunday.
"We will definitely remain in Baidoa. If we go anywhere, it will be to [the capital] Mogadishu. Once they get defeated, they will run away. Then we will move to Mogadishu, where the people are waiting for us," he said.
Gedi said foreign Muslim fighters had recently poured into Somalia, which he said confirmed the government's accusations that the Islamic courts movement was led by terrorists.
"Their numbers have doubled in just the last few weeks to about 8,000. Only in the Dinsoor area on Sunday, where we had the worst fighting yet, there were more than 4,000 foreign fighters," he said.
Gedi said government forces had photographs of three slain foreign Arab fighters - whose nationalities could not be identified - and had captured an Afghan flag on the battlefield.
Gedi said: "The presence of international terrorists makes this a global issue. These people only want power through bloodshed."
Gedi said that the government was grateful to Meles Zenawi, the Ethiopian prime minister, for his country's support.
Addis Ababa, which had previously acknowledged sending only military trainers to Baidoa, said on Sunday that it was at war with the Islamic courts and had sent forces into Somalia "to protect the sovereignty" of Ethiopia.
Kenya is bracing itself for a flood of refugees, and aid agencies are seeking to get emergency food and supplies into affected areas.
Gedi called for the acceleration of a UN-endorsed plan to send African peacekeepers into Somalia.
"I think that must happen. It is a global responsibility," he said.