The central bank is voluntarily signing the sector up to the Basel III reforms, aimed at strengthening the regulation, supervision and risk management of banks and due to be fully implemented within the European Union by 2027.
But the country's institutions are at odds over what criteria they should use to conduct risk assessments of borrowers under the Basel III framework.
The central bank wants to use in-house assessments, while the finance ministry says the capital buffers banks will require under the new rules should be based on domestic agencies' credit ratings.
The domestic agencies, whose assessments are not recognised internationally, have grown in influence since 2014, when Russia was subject in western sanctions that have triggered sovereign ratings cuts by the main international agencies.
Top Russian borrowers including Gazprom, Tatneft and Novatek have backed the finance ministry and asked Putin in a letter to do likewise.
Oreshkin said that, in late July, Putin gave his ministry and other officials a month "to study this and see what could be changed."
According to the companies' letter, using domestic ratings as a reference point would allow banks to cut lending rates, strengthen financial stability and ease the refinancing of external debt.
"The companies' concern could be understood: they could not forecast how accessible the external debt market could be due to the sanctions and aim to broaden availability of a loan inside Russia's financial system," Oreshkin told Reuters.
Russia is not obliged to follow the Basel III rules and some of its banks have publicly called on the central bank to abort the switch or change risk assessment rules.
The central bank, which has replied that it is committed to Basel III, says its approach of in-house risk assessment allows the system to "free up much more capital to lend to the economy."
Critics say Russia's domestic ratings lack in-depth statistics on defaults and cover a limited number of companies, but the finance ministry argues that without the central bank's support domestic ratings cannot develop.
"No-one is calling for... a widespread decrease in capital requirements for all assets, this would lead to a too high risk accumulation," Oreshkin said. "But in cases where borrowers' low risks allow decreasing capital requirements this makes sense.".
Kremlin spokesman Dmitry Peskov declined to comment on the letter.
(editing by John Stonestreet)
By Elena Fabrichnaya and Katya Golubkova