Several other people were wounded in the clashes that police say were unrelated to peace talks being held in Sudan between Somalia's weak transitional government and the country's increasingly powerful Islamic movement.
Police say they moved to evict militias who had set up at Baidoa's airport after having been dismissed as airport security workers.
The prime minister, Ali Mohamed Gedi, said he and his government regretted the incident, but said it had been necessary to ensure safety at the airport.
"The government has plans to set up a camp at the airport, which the militiamen had occupied," Gedi said. "We want policemen to take control of the airport."
Earlier, police and witnesses said 12 people - seven militia and five government security forces - had been killed in the incident.
The fighting came on the third day of talks in Khartoum aimed at easing tensions between the largely powerless government and the newly dominant Islamists that threaten to plunge the already anarchic country into further chaos.
Gedi says his government
regretted the deaths in Baidoa
The Islamists, who seized the former capital Mogadishu from warlords in June and have rapidly expanded their territory to include much of southern Somalia, pose a growing threat to the limited authority of the internationally backed government.
Arab League mediators are attempting to broker a compromise between the two sides, who are deeply split over several key issues, including the proposed deployment of regional peacekeepers.
They are also at odds over the reported presence in Somalia of Ethiopian troops, denied by Addis Ababa, allegedly sent to the country to protect the government from Islamist attacks.
On Sunday, the government proposed integrating its security units with Islamic militia to form a new national armed force as part of a power-sharing scheme. The Islamists have yet to respond.
The Islamists claim their battlefield successes entitle them to form their own government, but say they recognize the legitimacy of the administration.