The BBC reports this, citing a copy of a position paper that Russia is distributing among UN members asking for support.
Voting at the UN Human Rights Council will take place next month.
In the document, Russia promises to find "adequate solutions to human rights issues" and seeks to stop the council becoming an "instrument which serves political wills of one group of countries." With such a formulation, Russia alludes to the West. The document also claims that Russia does not want that group "punishing non-loyal governments for their independent and external policy".
In addition, Russia blames "the United States and its allies" for its loss of membership.
The BBC reminds that the UN Human Rights Council is based in Geneva and consists of 47 members, each of whom is elected for a three-year term. In the next election, which will take place on October 10, Russia will compete with Albania and Bulgaria for two seats on the council, which are reserved for Central and Eastern European countries.
The vote will be attended by all 193 members of the UN General Assembly in New York. Diplomats shared that Russia is waging an aggressive campaign, offering small countries grain and weapons in exchange for their votes. Thus, according to officials, it is possible that Russia could return to the Council.
A report this month by three campaign groups - UN Watch, the Human Rights Foundation and the Raoul Wallenberg Center for Human Rights - concluded Russia was "unqualified" for membership of the Human Rights Commission.
"Re-electing Russia to the council now, while its war on Ukraine is still ongoing, would be counterproductive for human rights and would send a message that the UN is not serious about holding Russia accountable for its crimes in Ukraine," the report said.
The UK also stated that it "strongly opposes" Russia's attempt to rejoin the Human Rights Council.
On April 7, the UN General Assembly suspended Russia's membership in the UN Human Rights Council.