A Moscow private clinic says it carries out female genital cutting "for medical reasons" and only on adult women.
In a statement on its website, Best Klinik denied "unreliable" reports about its "clitoridectomy service".
Earlier the Russian news site Meduza claimed that the clinic had also advertised the procedure for girls.
The report triggered heated debate on Russian social media. Female genital mutilation (FGM) is a crime in the UK; the UN says it violates human rights.
FGM - defined as partial or total removal of the external female genitalia for non-medical reasons - can cause severe bleeding and other serious complications, the UN's World Health Organization (WHO) says. FGM has no health benefits, the WHO adds.
In its statement, Best Klinik insisted it was providing a "clitoridectomy" service only for women aged 18 or older "in response to requests from patients who have a corresponding referral from a doctor".
The procedures are done at a clinic near Baumanskaya metro, in northern Moscow. Best Klinik also has two other clinics in the Russian capital.
Clitoridectomy - sometimes called "female circumcision" - can be carried out for medical reasons, but such cases are rare.
A Russian human rights group, Stichting Justice Initiative (SRJI), documented cases of FGM involving girls in Russia's Dagestan region, in the North Caucasus, in 2016.
The region's Muslim leader, mufti Ismail Berdiyev, said FGM was practised in some Dagestani villages and that it was necessary to curb women's sexuality.
SRJI says human rights lawyers now plan to ask the Russian Prosecutor General's office to investigate Best Klinik.
On Facebook a leading Russian women's rights activist, Alyona Popova, also urged the authorities to investigate the clinic's activities.
Best Klinik has not yet responded to a BBC request for clarification about its "clitoridectomy service".
SRJI's 2016 report on Dagestan prompted a Russian MP, Maria Maksakova-Igenbergs, to introduce a bill that would criminalise FGM.
But the bill did not become law, so FGM - which can be fatal - is not yet a crime in Russia.
The WHO says FGM is most common in western, eastern and north-eastern regions of Africa, in parts of the Middle East and Asia, and among migrants from those areas.
It says more than 200 million girls and women alive today have suffered FGM, in 30 countries.