A Somalia warlord has been arrested and deported from Kenya, after it said it would no longer host those who "destabilise" its lawless neighbour.
Abdirashid Shire Ilgayte was led away from his Nairobi hotel
Abdirashid Shire Ilgayte, a member of the alliance defeated by an Islamic militia in recent fighting, was led from his Nairobi hotel by police.
Kenya has played host to Somali peace talks involving almost all faction leaders, for the past three years.
The Islamists control Mogadishu but the warlords are said to be regrouping.
The BBC's Mohammed Olad Hassan in Mogadishu says the warlords of the Anti-Terror Alliance are strengthening their positions in Jowhar, 90 kilometres (56 miles) to the north-west.
On Tuesday, thousands of north Mogadishu residents demonstrated against the Union of Islamic Courts.
But BBC Somali Service editor Yusuf Garaad Omar says the Islamists are generally far more popular than the warlords, who are hated for their role in Somalia's 15-year civil war.
Islamist leader Sharif Shaikh Ahmed told the BBC on Tuesday that they would not impose a Taleban-style Islamic state in Somalia.
President Bush has expressed concern over the recent unrest and has warned the US will ensure Somalia does not become a safe haven for terrorists.
"Obviously when there's instability anywhere in the world we're concerned. There is instability in Somalia," Mr Bush said on Tuesday.
"First concern of course would be to make sure that Somalia does not become an al-Qaeda safe haven, doesn't become a place from which terrorists plot and plan," he added.
The US was accused of backing the warlords but has neither confirmed nor denied the persistent reports.
Sharif Shaikh Ahmed is seen as a relative moderate
Sharif Sheikh Ahmed told the BBC Arabic service that the Islamic Courts were not a movement.
"They are a kind of popular revolution by the Somali people after 16 years of anarchy and killing, plunder and kidnapping," he said.
"This body is not a political one. Rather we want to give power back to the Somali people so it can make its own decisions and decide its own destiny."
The violence in Mogadishu has been the most serious for a decade with some 330 people killed and about 1,500 injured in the past month.
It began when warlords who had divided Mogadishu into fiefdoms united to form the Anti-Terrorism Alliance to tackle the Islamic courts, who they accused of sheltering foreign al-Qaeda militants.
The Islamic courts deny this. They were originally set up in Mogadishu as a grassroots movement by businessmen to establish some law and order in a city without any judicial system.
The Islamic militia warns it is now within 20km (12 miles) of Jowhar, the town where the defeated warlords fled.
However, clan elders have warned the Islamists not to attack Jowhar.
Prime Minister Ali Mohammed Ghedi has welcomed the Islamists' victory and wants to hold talks with them.
His government is based in Baidoa 250 kilometres (155 miles) but only controls a small part of the country.