"In the course of the special operation, six active members of an illegal armed group were eliminated ... Weapons and ammunition were found in the house," Ruslan Alkhanov, the Chechen interior minister, was quoted as saying.
The two fighters killed near the city of Nazran in Ingushetia were also trying to escape security forces operation, news agencies reported, citing the local branch of the Russian FSB security service.
"Two fighters were eliminated this morning when trying to escape a section of forest that had been cordoned off," an FSB spokesman reportedly told the Interfax news agency.
Islamist fighters have been battling pro-Kremlin authorities and Russian security forces in a low-level insurgency in the overwhelmingly Muslim regions of Chechnya, Dagestan and Ingushetia for years.
But Chechnya has been relatively stabilised since Ramzan Kadyrov, the Kremlin-backed president, took power in 2007, leading Moscow to declare an end to military operations in the republic in April.
The latest violence came a day after representatives of Chechnya's Kremlin-backed president ended three days of talks with the self-declared government-in-exile in Norway.
"We have been consulting on the total political stabilisation of the Chechen Republic and the final consolidation of the Chechen society," Dukuvakha Abdurakhmanov, the leader of the Chechen parliament, said after the meeting in Oslo.
However, neither he or Akhmed Zakayev, the prime minister of the so-called government-in-exile in London, refused to give any further information about the issues that were discussed.
They agreed to meet again in the British capital within the next 10 days.
Ivar Amundsen of the Chechnya Peace Forum human rights group said it was the first time there had been "a serious political dialogue between the Russian-installed regime in Chechnya and the government-in-exile".
"This meeting has been authorised not only by Kadyrov himself ... It has been happening in perfect co-ordination with the highest leadership in the Kremlin," he said.