Security forces have killed four people accused of extremist activity while three Russian soldiers have been shot dead by gunmen in new violence that is gripping areas near Chechnya. Officials in Dagestan, on Chechnya's eastern border, said police and troops had surrounded a house overnight after observation suggested it was a centre for extremist activity. The occupants refused to surrender and, after children were allowed to leave, a gunbattle erupted, lasting until after dawn. Four men were killed and three women were taken into custody in the regional capital, Makhachkala.Meanwhile, in Ingushetia, to the west of Chechnya, Interfax news agency said that rebels had opened fire with machine guns on a car carrying Russian servicemen, killing three of them. The agency, quoting prosecutors, said a number of soldiers had been injured.