Ramzan Kadyrov, the Kremlin-backed leader of Chechnya, refuted allegations of his involvement in Estemirova's death and said he co-operated with her despite the fact that "she never had any honour, dignity or conscience".
Cherkasov said Kadyrov has demonstrated his enmity toward "rights defenders who are simply doing their job".
Jane Buchanan, of Human Rights Watch, told Al Jazeera: "We are extremely worried about the fate of Zarema and her husband.
"The authorities in Chechnya have shown themselves to be very intolerant of criticism. Natalia Estemirova had been herself threatened by Kadyrov in the past and he was not happy about the reporting she was doing exposing human rights abuses ... it's frankly a hostile environment to begin with.
"These are just outrageous crimes, the abduction and killing of Natalia Estemirova in a country that aspires to democratic standards is just appalling."
Speaking to the AFP news agency, another senior human rights worker and a former colleague of Sadulayeva said: "A gang came into her office around midday while she was working and then forced her into a car."
"There has been no news of her since," the colleague said, asking not to be named.
Cherkasov said Alik Djibralov, Sadulayeva's husband, had been jailed for four years for links to illegal armed groups and had married Sadulayeva two months after leaving prison.
'Let's Save the Generation' works with young people in Chechnya who have been marginalised, helping them get back on their feet to prevent them joining any of the armed groups in the unstable region,.