Somalia's interim prime minister, Nur Hassan Hussein, has met elders of the Hawiye clan, who are influential in the capital, as part of his peace efforts.
Checkpoint soldiers have been threatened with beheadings
He discussed his recently-outlined plan to restore stability. Both sides described the meeting as a stepping stone towards reconciliation.
It is not clear how much influence the elders have with the insurgents.
The most powerful group, al-Shabab, has said it will continue fighting. Most of its members are Hawiye.
Over the past year, the capital, Mogadishu, has been rocked by almost daily violence between Islamist insurgents and Ethiopian troops supporting the Somali government.
In the latest violence, four people, including three government soldiers are reported to have been killed in Mogadishu after gunmen in a vehicle open fire on government soldiers stationed at a junction.
The meeting is the first between the government and members of the Hawiye Cultural and Unity Council, says the BBC's Mohamed Olad Hassan.
He says many of the elders have been sharply critical of government policies and came out of hiding to attend the talks at Mogadishu International Airport under the security umbrella of African Union forces.
On Monday, the prime minister met business leaders in the capital.
Al-Shabab has become increasingly active, not only fighting in Mogadishu, but carrying out hit-and-run attacks throughout central and southern Somalia.
The Islamists are responsible for hit and run violence
In the past few weeks, al-Shabab has attacked a number of strategic towns, including Dinsor in the south-west and Bur Hakaba, near the seat of parliament in Baidoa.
A pattern is emerging whereby the militia briefly occupy the town, often killing a number of people, then withdraw with arms, ammunition and military vehicles seized from Somali government and Ethiopian troops.
Al-Shabab denies links to al-Qaeda and has distanced itself from the Somali opposition based in Eritrea, saying it is too secular.