In a report released on Monday, the Brussels-based group said the Mogadishu cell was led by a young Somali trained in Afghanistan, where al-Qaida was once based.
The armed outfit "announced its existence by murdering four foreign aid workers in the relatively secure territory of Somaliland between October 2003 and April 2004", the report added.
The International Crisis Group (ICG), which tracks conflicts around the world, said the threat of "terrorism" inspired by an extremist interpretation of Islam "in and from Somalia is real".
It added that al-Qaida contributed to attacks on US and UN peacekeepers in Somalia in the early 1990s and used the country as a transit zone for attacks on neighbouring Kenya and as a hiding place for some of its leading members today.
Somalia has been without a central government since clan-based regional leaders overthrew Mohamed Siad Barre in 1991.
A new transitional government was formed last year during peace talks in neighbouring Kenya, but the administration has failed to relocate to Mogadishu because the city is considered unsafe.
In March, United Nations experts monitoring an arms embargo on Somalia reported that Islamic hardliners, including a group with alleged ties to al-Qaida, was importing high explosives, mines, hand and rifle-fired grenades, anti-tank weapons and ammunition and anti-aircraft guns and ammunition.
In the latest assessment, the ICG did not name the Mogadishu cell, but said it is led by Aden Hashi Ayro. Its members had "little or no religious authority ... seem to be organised exclusively to conduct urban insurgency and terrorism operations without a clear political aim".
The group is also believed to have helped al-Qaida operatives in Somalia with logistics, jobs, identities and protection and to operate training sites in the Banaadir and Lower Shabelle regions, according to the report.
The ICG said Western governments, led by the US, were building up counter-terrorist networks headed by Somali faction leaders and former military or police officers and by working with the security services in breakaway Somaliland and semi-autonomous Puntland.
Neighbouring Ethiopia had also sent in counter-terrorism operatives.