MOGADISHU (Reuters) - At least 13 people were killed and scores wounded in the Somali capital Tuesday as Islamist rebels battled police and African Union peacekeepers throughout the day.

Witnesses said battles that began mid-morning were still going on at dusk. Both sides fired heavy machine guns and artillery and the insurgents unleashed volleys of mortar bombs at the hill-top Villa Somalia presidential palace.

It was the worst fighting in weeks in Mogadishu.

Representatives of the government and various Islamist factions engaged in the fighting refused to comment. Workers at the city's main hospital said dozens of wounded were admitted.

Residents put the death toll at 13 while local Shabelle Media reported 15 people had been killed. As usual in Mogadishu, the vast majority of those hurt were civilians.

A mother and her baby died after a shell landed on their house, said local man Abdirizak Mohamed. Their flesh was so mangled we did not know what to carry.

More than 16,000 civilians have been killed in the two-year-old insurgency, one million people have been driven from their homes, more than a third of the population depend on aid, and large parts of Mogadishu lie empty and destroyed.

The latest violence broke out after hardline Islamists al Shabaab said they would mount more attacks on the AU troops after killing at least 11 Burundian soldiers Sunday.

Burundi buried those peacekeepers Tuesday and declared five days of national mourning. The opposition in the small central African country has called for its soldiers to be withdrawn from harm's way in Somalia.

A two-day meeting of the AU's Peace and Security Council called for an urgent reassessment of the mission's mandate so it could adapt to conditions on the ground.

Eritrea, which the United States has accused of funneling weapons to Somalia's Islamists in the past, called for the AU peace force, AMISOM, to be pulled out.

It is imperative to get rid of any force deployed in Somalia under the pretext of 'peacekeeping mission', Eritrea's foreign ministry said.

SHABAAB THREAT

Asmara also criticized the new Somali government of President Sheikh Sharif Ahmed, a moderate Islamist, accusing him of betraying the struggle to liberate his homeland.

Any government formed ... be it on the part of regional and international organizations or goodwill parties, can never constitute legal representation of the Somali people, it said.

Al Shabaab gained support as one of many insurgent groups waging war against Ethiopian troops propping up the anarchic country's previous government. An Ethiopian withdrawal in January placated some Somalis, but al Shabaab has now turned its fire on AMISOM and the new government.

Experts hope the inclusion of many moderate Islamists in the new Somali administration may marginalize hardliners like the group, which is on Washington's list of terrorist organizations and is known to have foreign fighters in its ranks.

But analysts are split over al Shabaab's strength.

Some say it could overrun the government, while others say it has only a few thousand fighters and has used the media and high profile strikes to project a more powerful image, despite waning support among traditionally moderate Somali Muslims.

In a recording posted online Monday, al Qaeda's second-in-command Ayman al-Zawahri urged Somalis not to fall for a secular constitution and said militants there would fight the U.S.-made government.

Somalia