Bamako , Mali ( CNN ) -- Islamists in control of northern Mali said they forced a man and a woman into two holes and stoned them to death for committing adultery in the lawless region . Witnesses watched quietly as Islamists executed the two by pelting them with rocks in the remote Aguelhok town , according to a local resident . `` I do n't know how many rocks they threw or for how long it went on before they were both dead , '' said Haman Maiga , a resident of Aguelhok who witnessed the stoning . `` No one dared to try and stop the Islamists . '' The woman had two small children , a boy and a girl , according to Maiga . A leader of a radical Islamic group in the region said Sharia law condemns relationships outside marriage . `` The man and the woman , who were both married ( to other people ) , were having an affair , '' said Aliou Toure , the Islamist commissioner in Gao . `` They were stoned to death , the punishment for infidelity , according to Sharia , Islamic law . '' The stoning Sunday is the first reported Sharia killing since al Qaeda-linked Islamists took control of the north . Read more : Is this al Qaeda 's 'last chance ' for a country ? Mali has been in a state of Chaos since a military ruler overthrew the democratically-elected president in March , shaking one of West Africa 's most stable democracies . The coup leader stepped down in May and transferred power to a civilian transitional government , but uncertainty looms . Ethnic Tuareg rebels and Islamist militants have taken advantage of the chaos to seize control of the northern portion of the country . Mali becoming bitterly divided . Aguelhok was among the first to fall when Tuareg rebels aided by Islamist groups occupied the region this year . Months later , two groups with ties to al Qaeda hijacked the separatist uprising by the local Tuareg movement . The two groups now control two-thirds of northern Mali , an area the size of Texas that includes the towns of Gao , Kidal and Timbuktu . Islamists have since imposed a harsh form of Sharia law that bans drinking , music and sports on television . Most residents in the area are Muslims , but have protested against the strict form of Sharia as Islamists remain determined to apply it . `` We do n't have to answer to anyone over the application of Sharia . This is the form of Islam practiced for thousands of years , '' Toure said . `` The fact that we are building a new country on the base of Sharia is just something the people living here will have to accept . '' In addition to the killing , Islamist militants have gone on a rampage for months , destroying sacred tombs in the region and vowing to target more . Read more : International outrage grows over destruction of Mali shrines . In July , they ordered residents to leave the area and razed two tombs in Timbuktu . Two months prior , elderly men kept watch over the main library after Islamists burned a different tomb in another attack in the same town . Islamist militants regard such shrines as idolatrous and thus prohibited in their religion . They especially target Sufi shrines , which they believe are sacrilegious . Sufism is a mystical dimension of Islam considered offbeat and frowned upon by Islamic hardliners . Defense official : U.S. needs to 'accelerate ' effort to help Mali . CNN 's Faith Karimi contributed to this report .
` ` No one dared to try and stop the execution , '' a witness said . The woman had two small children , according to a local resident . Radical Islamic leader says it is punishment for infidelity . Chaos have swept Mali since a coup against the government in March .