At least 20 people have been killed and more than 40 injured in fighting in the Somali capital, Mogadishu.
The Islamists made rapid advances in June
The Union of Islamic Courts, which controls most of the city, is attempting to take a southern area held by warlord Abdi Qeybdid.
Fighters have been exchanging mortar, rocket and machine-gun fire.
The militia ousted most warlords from the capital in June, in an effort to restore order. It has been accused of al-Qaeda links - which it denies.
BBC regional analyst Martin Plaut says the battle under way in Mogadishu is a fight to the finish.
Analysts say peace talks between the government and the Islamic courts, which are due to resume in Khartoum, could now be under threat.
The Islamic courts are trying to push the warlords out of their last strongholds.
But in an interview with the BBC, the interior minister of the transitional government, Hussein Aideed, said the government was in control of the city and the Islamic courts had suffered major losses.
He said the ceasefire agreed between the parties two weeks ago in talks brokered by the Arab League had been broken by the Islamic Union, and the government would now only deal with moderate elements within it.
Mr Aideed's forces have joined Abdi Qeybdid's fighters, who are from the same clan.
"This was an unprovoked attack, and we have the will and the support of the Mogadishu population, and we control Mogadishu and not them," he said.
The fighting has focused on the Medina district, through which traffic to the south travels.
Much of southern Somalia is also held by the militia and its allies, and the group is hoping to strengthen its grip on the country.
Fighters of the Islamic courts are said to be well armed, and reportedly receiving support from neighbouring Eritrea.
The weak, UN-backed government is based in Baidoa, 200km from Mogadishu.
It is seen as being close to Eritrea's rival, Ethiopia.