MOSCOW — A Russian newspaper published extracts yesterday from an unpublished article by the investigative journalist Anna Politkovskaya that could hold vital clues to solving the murder of one of the Kremlin’s foremost critics.

As so often in the past her theme was the abuse of human rights in Chechnya, the province that President Putin has spent most of his presidency trying to suppress.

Politkovskaya, a mother of two who was shot dead outside her flat last Saturday, told the story of Beslan Gadayev, a Chechen accused of terrorism who was extradited from Ukraine in August.

In the incomplete article, published in the Novaya Gazeta newspaper, Politkovskaya accused the Moscow-backed authorities in Chechnya of using torture to extract fictitious confessions of terrorism that would please the Kremlin.

She quoted from a letter Mr. Gadayev sent her on August 29 that detailed the treatment he underwent at the hands of Chechen investigators.

“Immediately, they attached wires to my little fingers,” she quoted him as saying. “In about two seconds, I felt electric shocks. Simultaneously, they were beating me all over with rubber batons. Unable to tolerate the pain, I started screaming, calling to God, and begging them to stop.”

The newspaper also published stills and part of a transcript from a video obtained by Politkovskaya that appeared to show the torture or execution of two men covered in blood being interrogated by unidentified and unseen members of a Chechen law enforcement agency.

Human-rights investigators have alleged that Russian forces and their Chechen allies led by Ramzan Kadyrov are conducting a campaign of indiscriminate violence in the province.

Some have blamed Mr. Kadyrov, who allegedly has threatened Politkovskaya in the past, for her murder. He denies involvement.

Others, however, have said the killing could have been orchestrated to discredit Mr. Kadyrov after he reportedly fell out with his Kremlin backers this summer.