The release of the report came as Russian authorities announced that 13 suspected fighters were killed and a police officer and a civilian wounded in an exchange of fire in Ingushetia's Malgobek district on Thursday.
"Twelve members of an unlawful armed formation were eliminated in a counter-terrorist operation," an official in the regional branch of the federal security service said.
Moscow says the anti-government fighters are financed from abroad and seek to destabilise the north Caucasus region, where two separatist wars in Chechnya have been fought since the early 1990s.
Critics of the government's policy say official corruption and high unemployment are the main reasons behind the instability and violence.
New leader praised
Dmitry Medvedev, the Russian president, dismissed local leader Marat Zyazikov, a former KGB officer handpicked by his predecessor Vladimir Putin, in October.
Zyazikov was blamed by both Kremlin allies and critics for mishandling the region.
Yunus-Bek Yevkurov, the new Ingush president, has promised to improve the region's economic situation and ensure justice for the people.
Alexeeva of the Helsinki Group credits Yevkurov with helping to bring about change.
"Considering that their heads of regions are appointed, not elected, we think the decision made by the authorities to change the president of this republic (Ingushetia) was very wise," she said.
"And most importantly, the choice was made in favour of a man with the reputation of being experienced, balanced and honest, which was a pleasant surprise, because the whole country is sick with corruption - but the Caucasus is even worse."