Thousands of people have fled the Somali capital after scores of people were killed over the weekend.
People left Mogadishu in taxis, cars and lorries piled with mattresses, suitcases and furniture on Monday, witnesses said.
Ali Sheik Yasin Fadhaa, the vice-chairman of the local Elman Human Rights Organisation, said: "Some of them do not know where to go. They need urgent help."
He said that his staff throughout Mogadishu had counted at least 5,200 people fleeing on Monday, taking the total since Saturday to more than 17,000 Somalis.
"I have no other option," Asha Yakob told The Associated Press news agency as she left the northern Mogadishu neighbourhood of Fagah.
"Those who are fighting seem to be foreigners. If they were Somalis, they would never kill innocent and poor people like me. They are enemies."
Heavy clashes were reported between troops and anti-government fighters in Fagah early on Monday.
"The fighting is very heavy and both sides are using machine-guns and anti-aircraft weapons," Mohamed Abdi, a police officer, said.
Later a mortar shell landed near a cafe in the north of the capital killing at least two civilians, witnesses said.
The latest fighting is the heaviest in months.
Anti-government groups have vowed to defeat the interim government of Sharif Ahmed, the president and former leader of the Islamic Courts Union, which controlled much of Somalia for several months in 2006.
"The onslaught against the government is being led by Hizb ul-Islam and al-Shaabab," Al Jazeera's Mohammed Adow reported from Nairobi, the capital of Kenya.
"They may have different views on how to run Somalia, but they are now united in knocking Sheikh Sharif [Ahmed] from power."
"They are saying he has betrayed them and has betrayed the cause of the Somali mujahidins
"They say he has sided with what is seen as the side of the Ethiopian government and the United States."
Sheikh Bashir Ahmed Salad, chairman of a religious panel trying to mediate between the two sides, said they were concerned over the deteriorating situation.
"We had been contacting both sides in the past week to avoid bloodshed, but they ignored our calls and engaged in fighting that led to civilian casualties," he said.
Ahmed has blamed foreign governments trying to destabilise the Horn of Africa nation for supporting the anti-government fighters.
"We have an Islamic government, but misled Somalis kill innocent people. These guys work for foreign countries that do not want us to be a peaceful nation," he said.
"I tell them to stop fighting. It is illegal to shed the blood of your innocent brothers."
Ahmed has been trying to broker peace with warring groups, but his administration wields little control outside Mogadishu and needs support from African Union peacekeepers.
Fighters opposed to the government see the 4,350 AU peacekeepers as "foreign invaders" and an obstacle to a lasting peace.