Estemirova's body was found on Wednesday in a wooded area in Ingushetia, the region neighbouring Chechnya, just hours after she was seized from her home in Grozny, the Chechen capital.
She had been shot twice in the head.
Orlov said on Thursday Kadyrov was "guilty for the murder of Natalia".
"Ramzan already threatened Natalya, insulted her, considered her a personal enemy," he said.
The 50-year-old was buried in a ceremony in Koshkeldy, a Chechen village, on Thursday, while about 100 mourners gathered to remember the rights activist, who was also a single mother, outside Memorial's office in Grozny.
Human rights supporters also gathered in Moscow to protest against her murder.
Dmitry Medvedev, the Russian president, said Estemirova "spoke the truth and openly, sometimes toughly, described some processes that happen in this country".
"That is the value of a rights activist. Even if these things are not pleasant and uncomfortable for the authorities".
Call for investigation
Ban Ki-moon, the UN secretary general, said he was "appalled" by the killing.
He called on Russian authorities to "conduct a thorough and impartial investigation in order to bring the perpetrators of this heinous killing to justice, and by so doing, to send a strong and unambiguous message that the targeting of human rights activists will not be tolerated."
Estemirova's body was found near the city of Nazran shortly after a number of men bundled her into a white vehicle outside her home, human rights activists said.
Memorial and Human Rights Watch (HRW) had earlier this month issued a report accusing Chechen security forces of punishing families of alleged fighters by burning down their homes.
After Russia ended a 10-year "counter-terrorism" operation in Chechnya earlier this year, it handed security responsibilities to Kadyrov.
He has also recently been given licence to target rebel fighters in neighbouring regions.
Russia's Gazeta newspaper reported on Thursday that Chechen authorities had complained about Estemirova's work.
"By coincidence, just before the murder, Chechnya's rights ombudsman Nurdi Nukhazhiyev called on Memorial's Grozny office chief to complain about Estemirova, saying she refuses to see positive changes and insists on bringing up dirt," it said.
In 2007, Estemirova was awarded the Anna Politkovskaya prize - named after the murdered Russian journalist - by the Nobel Women's Initiative, a group established by female Nobel Peace Prize laureates.