* Fighting has intensified since Kampala attacks
* AU forces help government troops push back rebels
By Abdi Sheikh
MOGADISHU, July 20 (Reuters) - Fighting between al Shabaab rebels and government forces in the north of Somalia's capital has killed at least 52 civilians and wounded scores over the past week, a local rights group said on Tuesday.
The violence in Mogadishu has intensified since al Shabaab suicide bombers killed 73 people watching the World Cup final in Uganda's capital and the festering conflict is likely to be high on the agenda at an African Union summit in Kampala this week.
Troops from Uganda and Burundi make up the roughly 6,300 strong African Union force protecting key sites in Mogadishu and there have been calls for their mandate to be widened so they can go on the offensive against the al Qaeda-linked insurgents.
"It is ceaseless fighting and shelling between government forces and al Shabaab in the north of Mogadishu," Ali Yasin Gedi, vice chairman of the Somalia-based Elman rights group told Reuters on Tuesday.
"At least 52 people died and 129 others were injured in this week's fighting."
Al Shabaab and another Islamist militia have been fighting the Western-backed Somali government since the start of 2007. They control much of the capital but have failed so far to drive President Sheikh Sharif Ahmed from office.
The African Union force, known as AMISOM, has stepped in at key moments to protect the president's palace and Uganda said last week it was ready to send another 2,000 troops to help take the fight to the rebels.
REBELS PUSHED BACK
Mogadishu residents said AU tanks and government troops made some advances on Tuesday, retaking areas lost to al Shabaab a day earlier, although civilians once again bore the brunt of shelling by both sides.
"Today we helped the government push the rebels back. It is within our mandate to protect and support the transitional federal institutions," AMISOM spokesman Barigye Ba-Hoku told Reuters on Tuesday.
On Sunday, a shell hit a building next to Koranic school between the presidential palace and the city's port, wounding 14 children studying there, witnesses said.
"The shrapnel penetrated into the school which was made of iron sheets," said Aden Bashir. "My sons sustained injuries in the head and hand."
At least 21,000 civilians have been killed since the start of the insurgency. Aid agencies and rights groups have become increasingly concerned about indiscriminate shelling and some have accused combatants on all sides of war crimes.
In April, the United Nations condemned the shelling of heavily populated areas by Somali forces, AU troops and the rebels -- who are fighting to impose their own harsh version of sharia law in the Horn of Africa nation.
Al Shabaab said the suicide attacks in Uganda on July 11 were to avenge the killing of civilians by African Union forces. (Additional reporting by Mohamed Ahmed; Editing by David Clarke)