"There is a fear among the population in the capital that the government will force its way into Mogadishu but we are not going to do that," Ali Ahmed Jamah, the information minister, said.
Ethiopian forces on Wednesday captured the town of Jowhar, 55km north of Mogadishu.
Islamic courts vow to fight
The Islamic Court Union, meanwhile, vowed to resist the government's advance, fight the Ethiopians and maintain security in Mogadishu.
"The security we are enjoying is very important and we cannot let violent people destabilise our city," Sheikh Sharif Sheikh Ahmed, the chairman of the courts' executive committee, told a press conference in Mogadishu.
The Islamists have so far not substantially resisted the Ethiopian advance but have instead withdrawn their forces to defend Mogadishu.
On Wednesday, leaders of the courts also said that they were inviting foreign Muslims to come to Somalia to fight the Ethiopian forces.
US support for Ethiopia
The US has also voiced cautious support for the Ethiopian offensive.
"Ethiopia has genuine security concerns with regard to developments within Somalia," said Gordon Johndroe, spokesman for the White House National Security Council.
The US government has accused the Islamic courts of harbouring al-Qaeda members and men suspected of bombing US embassies in Tanzania and Kenya in 1998.
The African Union and the Organisation of the Islamic Conference have called on Ethiopia to withdraw.
The UN Security Council failed to agree on a statement that Qatar had proposed, which would have called for all foreign forces to withdraw from Somalia.