BAMAKO (Reuters) - Islamist fighters in the northern Malian city of Timbuktu executed a man on Tuesday for murdering his neighbor in an application of sharia, Islamic law, the Islamist group and witnesses said.

Armed Islamist groups, some with links to al Qaeda, have controlled the northern two-thirds of Mali since April, when they hijacked a rebellion launched by ethnic Tuareg separatists.

They have since imposed sharia in many of the areas under their control.

A spokesman for Ansar Dine, which controls Timbuktu, said the executed man was a member of the group.

"He turned himself in...He was judged, condemned to death and executed this evening. He was shot in the same way he shot his victim. This is what sharia says," Sanda Ould Boumana told Reuters.

The United Nations Security Council last week voiced concern about human rights violations by rebel and militant groups in northern Mali.

West African countries from regional bloc ECOWAS have requested a U.N. mandate for a possible military intervention in the vast, arid country.

Progress has been hampered by infighting among politicians and military officials in the government-held south and disagreements among international partners.

(Reporting Adama Diarra and Tiemoko Diallo; Writing by Joe Bavier; Editing by Michael Roddy)