The spokesman of the Islamic courts, Abdirahim Isse Adow, said the weapons they use are seized from Ethiopian forces and Somali government troops during times of battle.
The spokesman also accused the international community and the UN for their role the importation of weapons into Somalia.
The accusations of the Union of Islamic Courts come at a time when a UN team monitoring the Somalia arms embargo issued a report confirming the illegal influx of weapons into Somalia.
The Islamic courts say they want to promote Islamic law rather than clan allegiance, which has divided Somalis over the past 15 years.
But Somalia is a strongly Islamic country and many people support the courts.
During the years of warfare and anarchy, many Somalis have increasingly turned to their faith for some sort of stability.
One visible sign is that before the civil war began in the 1980s, very few women wore headscarves in Mogadishu.
Now, almost every woman wears a headscarf and an increasing number are wearing veils covering their faces, with just narrow slits for the eyes.
Even those Mogadishu residents who are wary of Islamic extremism may welcome a single group being in control of the capital for the first time in 15 years, saying there will at least be some authority.
And most will prefer Islamic preachers to the warlords who have repeatedly fought over and in many cases systematically looted the city since 1991.
BBC Somali analyst Yusuf Garaad Omar says the warlords were hated – even more so because of the widespread belief that they were being backed by the US.
The US has not been well thought of in Somalia since its humanitarian intervention went disastrously wrong – leading to the death of maybe 1,000 Somalis and 18 US troops in 1993