One of the blasts on Monday afternoon occured outside a hall where Abdullahi Yusuf, the Somalia president, had given a speech ten minutes earlier, a local journalist said.
Many politicians were still in the buillding where they had been discussing forming a new parliament to shore up the government which has been challenged by the rise of the Islamic Courts Union, a militia controlling much of the country.
A second explosion, apparently a car bomb, targeted the president convoy.
"Five people were killed from the presidential convoy and three wounded," Ismail Hurre, the foreign minister, said.
Six attackers were also killed and two captured in a gunbattle with Yusuf's bodyguards after the explosion, he added.
"This was an attack aimed at assassinating the president to destabilise the government."
Among the dead was the president's brother, the Associated Press news agency reported, quoting government officials.
The explosions sent huge balls of flame into the sky and destroyed eight cars, including three that were in the president's convoy, witnesses said.
The Supreme Council of Somalia, the Islamist militia that has gained control of Mogadishu, the capital, and much of the south of the country in recent months, denied carrying out the attack.
"We are very sorry for the incident that took place in Baidoa," said Abdurahim Ali Muddey, a spokesman for the group.
'Enemies of Somalia'
"Those who carried out this attack are the enemies of Somalia, they wanted to undermine our ability to resolve differences by ourselves"
Abdurahim Ali Muddey, a spokesman for the Supreme Council of Somalia
"Those who carried out this attack are the enemies of Somalia, they wanted to undermine our ability to resolve differences by ourselves," he added.
Earlier, speaking to Aljazeera television from Mogadishu, Sheikh Sharif Sheikh Ahmad, chief of the Islamic Courts Executive Council in Somalia, said, "we reject any form of violence as we look forward to achieving peace".
"It seems that there were many conspiracies plotted against this country."
"I accuse foreign countries particularly Ethiopia of planning for such an act as it seeks to get its troops into Soamlia and to justify its position before the UN."