Thousands of Somalis took to the streets of their capital Tuesday, some demonstrating for Islamic militiamen who claimed control of Mogadishu a day earlier in a setback for U.S. counterterrorism policy, others calling for the fundamentalists to get out.

Mogadishu has been convulsed for months as the Islamic Courts Union, which has alleged links to Al-Qaeda, 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 is raising fears that Somalia could fall under the sway of Usama bin Laden's terrorist organization. But Tuesday's protests show it may be difficult to keep control of the capital, and that the courts likely still have to negotiate with the clan leaders who have been controlling 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!"

"If the so-called Islamic courts don't stop invading our territories ... the country will return to civil war," said Sheik Ahmed Kadare, an Abgal clan elder. The clan did not give a timetable for a potential attack.

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

Tuesday's Abgal rally appeared to be an attempt to redefine the latest conflict in the capital as a competition between 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 in order to raise money and goodwill for their bid to take over the country.

The Islamic militia kept defensive positions about 2 kilometers (about a mile) from the Abgal protest and did not move in to stop it. They also held their own rally nearby, vowing to keep fighting until Islamic Sharia 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 have said a government based on Islamic law will restore order to Somalia and they 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 had links to terrorists.

U.S. officials said recently that Islamic leaders in Mogadishu are sheltering three al-Qaeda leaders indicted in the 1998 U.S. Embassy bombings in Kenya and Tanzania. The same al-Qaeda cell is believed responsible for the 2002 suicide bombing of an Israeli-owned hotel in Kenya, which killed 15 people, and a simultaneous attempt to shoot down an Israeli airliner over Kenya.

The U.S. officials, speaking on condition of anonymity because of the sensitivity of the issue, have confirmed cooperating with the secular warlords defeated by the militiamen Monday. The Bush administration has not confirmed or denied giving money to the alliance, saying only that it supports those who fight terrorism.

The United States has not carried out any direct action in Somalia since the deaths of 18 servicemen in a 1993 battle in Mogadishu depicted in the film "Black Hawk Down."

The battle between the militia and the secular alliance had been intensifying in recent months, with more than 300 people killed and 1,700 wounded — many of them civilians caught in the crossfire of grenades, machine guns and mortars.

The two sides began competing for influence in earnest after a U.N.-backed interim government slowly began to gain international recognition. But the weak government, wracked by infighting, has not even been able to enter the capital because of the violence. Instead, it's operating out of a base in Baidoa, 155 miles from Mogadishu.

Weapons prices soared there Monday amid fears the militia could head to Baidoa next.

Meanwhile, two leaders of the secular alliance, Bashir Rageh and Muse Sudi Yalahow, pledged their loyalty to the Abgal clan Tuesday.

"Our clan has agreed to defend our land and we will fight the courts hiding under the cloak of Islam and trying to fool our people," said Rageh, who arrived at the demonstration with Yalahow, escorted by Abgal militiamen.