(Adds U.S. comments)

By Sahal Abdulle

MOGADISHU, April 23 (Reuters) - Somalis fled a sixth day of shelling in Mogadishu, desperate to leave a capital where a rights group said allied Somali-Ethiopian troops killed 37 people on Monday in an offensive to wipe out Islamist rebels.

That brought the death toll from the latest violence to at least 267, according to the local Elman Peace and Human Rights Organisation, which tracks casualties from hospitals, families and counts on the street, where bodies rot in the sun.

The U.N. refugee agency UNHCR warned of scenes of growing chaos as hundreds of terrified residents carried on fleeing the coastal city and crowds of tired, hungry people demanded help.

"Many are traumatised because of relatives killed ... and some children are crying because they have been separated from their parents while fleeing and don't know how to find them," said one UNHCR staff member, declining to be named.

The United States said it was concerned about the growing humanitarian crisis in Somalia, triggered by the biggest exodus from the capital since warlords overthrew a dictator in 1991 and plunged the Horn of Africa country into 16 years of lawlessness.

Nearly half a million people have fled Mogadishu, thousands sleeping under trees or in the open in surrounding towns and villages. Before the fighting, Mogadishu's population was estimated at between 1-2.4 million people.

CATASTROPHE

Humanitarian workers have warned of a looming catastrophe, with diseases like cholera already rife.

"It's very clear that there is a humanitarian crisis coming out of the conflict that is taking place in Mogadishu," Jendayi Frazer, U.S. Assistant Secretary of State for African Affairs, told reporters in Washington.

Frazer urged all sides to reach a ceasefire and said the United States was working with the Somali government, U.N. agencies, the Ethiopians and others to try to help people affected by the fighting.

She dismissed suggestions the international community was not devoting enough attention to Somalia. "There is not a lack of action on Somalia," she said.

UNHCR said Afgooye, 30 km (19 miles) west of Mogadishu, was jammed with more than 41,000 displaced people and that the crowds were becoming increasingly difficult to control.

The Elman group said 18 civilians and 19 insurgents were killed on Monday. There was no word of Ethiopian and Somali military casualties.

Civilians have been the main victims and hospitals are so crowded the wounded are tended in tents or under trees.

The government is struggling to gain full control of the capital four months after ousting rival Islamist leaders who ruled much of southern Somalia for the second half of 2006.

Four days of fighting at the end of March killed at least 1,000 people, again mostly civilians.

Prime Minister Ali Mohamed Gedi has said there will be no let-up in the offensive until the government crushes Islamist rebels backed by foreign jihadists and disgruntled militiamen from the capital's dominant Hawiye clan.

He said neighbouring Eritrea was interfering in Somalia, prolonging the fighting.

Frazer said: "Eritrea has not been playing a constructive role in Somalia. They continue to fund, arm, train and advise the insurgents."

Eritrean officials could not be reached immediately for comment but have denied such allegations in the past.

An African Union force of about 1,500 Ugandan peacekeepers, working with Gedi's government and also targeted by the insurgents, has so far failed to stop the bloodshed. (Additional reporting by Farah Roble; Sahra Abdi Ahmed in Kismayu; Daniel Wallis in Nairobi)

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