"They wanted to undermine the peace process and they missed their target and killed children," said Mogadishu mayor Mohamed Dheere.
At least two people died earlier, after insurgent attacks on a market.
The conference has been repeatedly postponed, with a boycott by Islamists and Mogadishu’s clan elders.
None of the 1,000 conference delegates were hurt in the attack.
Prime Minister Ali Mohamed Ghedi said it was "historic" to be holding the conference, due to last a month, in the Somali capital.
The sky was lit by the explosions
The delegates were to discuss an 11-point agenda, including clan divisions and holding elections, said conference spokesman Abdirahman Mohamud Shift, according to the AP news agency.
The international community has urged the government to include moderate Islamists in the conference in order to bring peace to Somalia.
But the Islamists and Hawiye clan elders refused to attend, saying the venue is not neutral, while Ethiopian troops remain in the country.
Ethiopia helped government troops oust the Union of Islamic Courts from Mogadishu last December.
Islamist leaders are instead holding a rival meeting in the Eritrean capital, Asmara.
President Abdullahi Yusuf has vowed that the talks would go ahead even if a nuclear bomb was dropped.
There was fierce fighting around Bakara market before the conference opened.
"The sky was lit by the explosions," grocery shop owner Mohamed Abdi told Reuters news agency.
"They were the heaviest attacks so far on the troops."
The BBC’s Mohammed Olad Hassan in Mogadishu says some people have fled the area around Bakara market, where attacks are common.
Several mortar shells landed near the conference venue on Sunday, injuring civilians, when the talks first began.
It was immediately postponed to give some of the delegates more time to arrive.