* Insurgents vow to avenge dead civilians
* At least 30 people killed by rockets on Thursday
* African Union peacekeepers deny responsibility
(Updates with President Museveni, paragraph 12)
By Abdi Guled and Ibrahim Mohamed
MOGADISHU, Oct 23 (Reuters) - Somalia’s hardline al Shabaab insurgents said they would strike the capitals of Burundi and Uganda in revenge for rocket attacks by peacekeepers from those countries that killed at least 30 people in Mogadishu.
"We shall make their people cry," Sheikh Ali Mohamed Hussein, al Shabaab’s self-styled governor of Banadir region, which includes Mogadishu, told reporters late on Thursday.
"We shall attack Bujumbura and Kampala ... We will move our fighting to those two cities and we shall destroy them."
Burundi and Uganda both have about 2,500 peacekeepers in the Somali capital for the African Union’s AMISOM force.
Reuters witnesses said they fired at least 35 rockets into the capital’s Bakara market area on Thursday after al Shabaab gunmen there launched mortar shells at President Sheikh Sharif Ahmed’s plane as he left the airport for a summit in Uganda.
The United States accuses the rebel group, which wants to topple Ahmed’s fragile U.N.-backed administration and impose its own strict version of Islamic law across the country, of being al Qaeda’s proxy in the failed Horn of Africa state.
AMISOM’s spokesman in Mogadishu, Major Barigye Ba-hoku, denied on Friday that the AU soldiers had fired any artillery and blamed Thursday’s civilian deaths on rebel bombs.
"We did not shell any place ... We are investigating and the Somali government is investigating too," Ba-hoku told Reuters.
"Al Shabaab wants to drag us into their war ... they shell us and then they also shell Bakara, then they tell people there it was AMISOM who killed civilians. We know their tactics."
Fighting in Somalia has killed 19,000 civilians since the start of 2007 and driven another 1.5 million from their homes, triggering one of the world’s worst humanitarian emergencies.
Western security agencies say Somalia has become a haven for militants, including foreign jihadists, who are using it to plot attacks across the region and beyond.
Ugandan President Yoweri Museveni warned al Shabaab not to try anything. "These terrorists ... if they attempt to attack us, they will pay very heavily," he told reporters in Kampala.
CIVILIAN DEATHS "DISASTROUS"
Speaking to Reuters in neighbouring Kenya, Somali Prime Minister Omar Abdirashid Sharmarke denounced the insurgents.
"They are firing from Bakara and even mosques. They are using people there as human shields ... We regret what happened. It is never our intention to hurt our own people," he said.
Thursday’s clashes were some of the heaviest to rock Mogadishu for weeks, and they underlined the difficulties facing the 5,000-strong AU mission.
While winning some hearts and minds by giving residents access to clean water and free medical treatment, AMISOM has been unable to do much more than secure the city’s airport, sea port, presidential palace and a few roads in between.
Its soldiers come under near-daily attacks from roadside bombs and rebel artillery, and last month al Shabaab hit their main headquarters with a twin suicide car bombing that killed 17 peacekeepers, including the Burundian deputy force commander.
"We do not take their threats lightly," Ba-hoku said. "Any attempt to attack Burundi or Uganda will be met with decisive action and will be defeated."
Several African nations had committed to send troops to reinforce AMISOM but have so far failed to do so, some saying in private that they are put off by the incessant violence.
Despite that, Mogadishu-based political analyst Abdikarim Omar said AMISOM was still better organised and armed than the rebels, and it should begin a drive to clear them from the city.
"They should launch a major offensive ... This endless shelling of commercial and residential neighbourhoods, the killing dozens of innocent people, is more disastrous than a two- or three-week operation." he told Reuters. (Additional reporting by Abdi Sheikh in Mogadishu, Abdiaziz Hassan in Nairobi and Frank Nyakairu in Kampala; Writing by Daniel Wallis; Editing by Giles Elgood)