Mogadishu, Somalia ? Thousands of Somalis took to the streets of their capital Tuesday, some demonstrating for Islamic militiamen who claimed control of Mogadishu a day earlier and others calling for the radical militia to get out.

Mogadishu has been convulsed for months as the Islamic Courts Union, which has alleged links to al-Qaida, strengthened its grip on this lawless country. Their advance Monday came despite U.S. support for a secular alliance of warlords that was opposing them.

The militia’s growing power has raised fears that Somalia could fall under the sway of al-Qaida. But Tuesday’s protests show it may be difficult to keep control of the capital, and that the Courts Union likely still has to negotiate with the clan leaders who have run the city for more than a decade.

The city’s largest and historically strongest clan, the Abgals, came out in force Tuesday and drew about 3,000 people to the northern part of the city, shouting “We don’t need Islamic deception!” and “We don’t want Islamic courts, we want peace!”

Somalia has been without a real government since largely clan-based warlords overthrew dictator Mohamed Siad Barre in 1991 and then turned on each other, dividing this nation of 8 million into rival fiefdoms.

The Abgal rally appeared to be an attempt to redefine the conflict in the capital as a competition among clans, rather than a religious battle, to build support for continued fighting if the Islamic militants do not retreat.

The Abgal leaders promised to set up new, clan-based courts in northern Mogadishu to replace those that the Islamic extremists have operated in recent years to raise money and goodwill for the militiamen’s bid to take over the country.

The Islamic militia kept defensive positions about a mile from the Abgal protest and did not try to stop it. It held its own rally nearby, vowing to keep fighting until Islamic law was enforced.

“Until we get the Islamic state, we will continue with the Islamic struggle in Somalia,” Sheikh Sharif Ahmed, chairman of Islamic Courts Union, told the crowd of about 500.

The Courts Union has said a government based on Islamic law will restore order to Somalia, and accused the secular alliance of warlords of being puppets of Washington and working for the CIA. Members of the alliance – most of whom were on the run after Monday’s defeat – said the Courts Union had links to terrorists.