"The Islamic courts announced they are in control of Mogadishu," resident Ali Abdikadir told Reuters, following a meeting with Islamic leaders. "They said they would work with residents to improve security in the capital."
An estimated 350 people have died since February in fighting between militias loyal to Islamic leaders, and warlords, drawn from a coalition of Somali clans, touting secularism.
The warlords have sought the backing of the United States, warning that Somalia could become a terrorist haven under Islamic rule, although some analysts have said that claim is more about getting money and aid from anti-al-Qaida American officials.
The United States is providing up to $150,000 a month in aid to the warlords, Somalia expert and former Clinton administration official John Prendergast told Reuters.
Monday's seizure of the city by Islamic militants brought a temporary peace to the capital, where daily gun fights have been raging for three months.
"The city is calm and we hope it will stay that way," 19-year-old resident Samira Jama told Reuters.
While Somalia's largely ineffective interim government has promised to bring security and improve infrastructure in the war-torn country, most of the services in Mogadishu and outlying areas have been provided by Islamic courts, some residents and analysts have said.
"The era of warlords in Somalia is over," one resident told Reuters. "This morning Mogadishu is under only one hand, the Islamic courts."
A spokesman for Somalia's government Abdirahman Dinari said officials hope to establish talks with Islamic leaders soon.
"I hope the Islamic courts will realize the importance of the government and talk to us. We are ready to talk to them in order to prevent further suffering of the innocent Somali people," he said.
The lawless Somali capital of Mogadishu was the subject of the 2001 movie Black Hawk Down, which depicted the true story of the killing of 18 U.S. Army Rangers on the streets of Mogadishu in 1992.
The United States pulled out of Somalia soon after the incident and has maintained only covert ties to the country since.
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