(Recasts with air strikes in south, adds rebel brigade withdraws in Sanaa)
SANAA, April 21 (Reuters) - Yemeni air force strikes killed 13 suspected al Qaeda-linked militants in the south on Saturday, local officials said, as the armed forces fought to quell a stubborn Islamist insurgency.
Residents said the aircraft had attacked suspected militant strongholds in Jebel Yasuf and al-Minyasa in the Lawdar area, where officials say more than 200 Islamist fighters have been killed in less than two weeks.
Militants have exploited a year of upheaval that severely weakened central government control over whole swathes of Yemen to strengthen their foothold in the impoverished state, particularly in the south.
Recently elected President Abd-Rabbu Mansour Hadi is also grappling with a southern seccessionist movement and a rebellion by Shi'ite Muslims who have effectively carved out a state within a state in the rugged northern province of Saada, on the border with Saudi Arabia.
An official said eight people were killed near the city of Saada on Saturday in a shootout between Shi'ite rebels known as Houthis and Sunni Muslim Salafis who attend a religious school in the area.
Fighting broke out when four Salafi students approached a checkpoint manned by Houthis on the outskirts of the city and shooting broke out, the official said. Four people died on each side and each accused the other of firing the first shot.
The Houthis have fought regularly with Salafis in Saada, accusing Riyadh of smuggling weapons to the Salafis because the two follow a similar creed. Salafis view Shi'ites as heretics.
Saudi Arabia briefly fought the Houthis in north Yemen after the Houthis grabbed a piece of Saudi territory in 2009.
The U.S. envoy to Yemen said earlier this year there were signs that Shi'ite Iran was becoming more active in Yemen. Iran denies interfering there, but Saudi Arabia says Iran is fomenting unrest among Shi'ites in eastern Saudi Arabia and in neighbouring Bahrain.
Separately, the defence ministry said an infantry brigade commanded by rebel General Ali Mohsen al-Ahmar had withdrawn from the capital, in line with a plan to demilitarise the streets of Sanaa.
Loyalist troops, tribal militiamen and soldiers who defected with Ali Mohsen last year divided Sanaa into warring zones of influence. Previous efforts to clear them from the streets have failed.
UNICEF expressed alarm at the number of children that had recently fallen victim to landmines in Yemen, identifying Abyan, Aden and Lahej in the south, Hajja in the north, and Sanaa in the centre as the worst affected provinces.
It said 13 children were reported killed and 12 maimed by mines or unexploded ordnance in the first three months of 2012 alone. (Reporting by Mohammed Ghobari; Writing by Isabel Coles; Editing by Tim Pearce)