Hundreds of residents fled Mogadishu Friday as fighting between government troops and hardline Islamist rebels erupted for a third day, injuring 19 civilians, witnesses said.

More than 40 civilians have been killed since Wednesday in the battles for control of the war-riven city.

Mogadishu Mayor Abdirizak Mohamed Nur urged residents to move out of the battle zones and announced that a planned government onslaught against the rebels was imminent.

"We call on residents to stay away from the fighting zones because the big offensive to sweep rebels from the whole city is imminent," Mohamed Nur told reporters.

Mogadishu residents had started fleeing the city after the embattled Somali government announced plans for the assault in January, but some returned after the offensive never came.

On Friday, the warring sides exchanged heavy artillery fire that flattened houses in a southern Mogadishu neighbourhood.

"Hundreds are fleeing the city today as clashes between Somali government and insurgents go into a third day," said Mohamed Moalim Kulow, a local resident.

"I have seen houses in several blocks in my neighbourhood completely destroyed by the heavy shelling and no one is left in that neighbourhood," Kulow said as he boarded a mini bus with his five children.

A medical official in the city's Daynile hospital said: "We have received 19 civilians who were injured in the shelling this morning. Three of them were seriously injured and one them was a child."

Violence erupted Wednesday when the Al Qaeda-linked Shebab fighters attacked their rivals in the north of Mogadishu, triggering an intense firefight that claimed the lives of at least 23 civilians.

In retaliation Thursday, AU peacekeepers backing the government troops drove tanks into a Shebab stronghold in the same area, raining fire on the rebels. More than 20 civilians were killed and scores wounded.

The Shebab claimed inflicting heavy damage on their rivals, who briefly occupied one of their frontlines in the north of the seaside city.

"We damaged some of the enemy's armoured vehicles in the clashes... They retreated to their positions with heavy losses yesterday," Shebab spokesman Sheikh Ali Mohamoud Rage told journalists.

"Their response is only shelling civilian-populated areas far away from the fighting zones," he added.

A resident from the area said residents were using all means to flee.

The UN refugee agency said in Geneva that more than 100,000 people have been forced to flee their homes across Somalia since the start of the year because of fighting, including the latest battle in Mogadishu.

Some 8,300 displaced people are also trapped in the capital, said the UN High Commissioner for Refugees (UNHCR), which added that Mogadishu clashes had uprooted 33,000 Somalis since February.

"As the fighting rages on, aid agencies cannot access and assist these extremely vulnerable IDPs (internally displaced people)," UNHCR spokesman Andrej Mahecic said Friday, calling the conflict "relentless and indiscriminate."

"Everybody in Arjantin neighborhood is fleeing. Some people are using carts, others are leaving on foot while those who can afford are fleeing on mini buses," said Hasan Diriye.

The Western-backed Somali government has been confined to just a few blocks in the capital after a deadly Shebab-led offensive last year.

On Tuesday, a senior US military officer voiced support for efforts by the Somali government to take control of the capital Mogadishu, saying it could help ease the country's chronic instability.