On Wednesday the group announced the resumption of its operations in Chechnya.
Memorial suspended its activities in the region in July following the murder of Natalya Estemirova, a researcher for the human rights group.
Orlov said: "We state today that we are resuming our activities in full volume on the territory of Chechnya. This uneasy decision was made as a result of consultations with our staff in the North Caucasus as well as with a large group of Russian and international human rights organisations".
Estemirova was abducted outside her home in Grozny, Chechnya's capital, on July 15 and found shot dead in the neighbouring republic of Ingushetia later the same day.
Her murder was followed three weeks later by the killings of Zarema Sadulayeva and her husband, Alik Dzhabrailov, who both worked for a Chechen charity.
'Freedom and democracy'
Kovalyov said "it is Europe's duty not to remain silent" in the face of Russian human rights abuses.
Joseph Daul, the chairman of the Christian Democrat EPP, the biggest group in the legislature, said: "I hope that this prize will encourage them to continue the fight for what we all believe in - freedom and democracy."
Alexeyeva, 82, and Kovalyov, 79, were both leading Soviet dissidents and contemporaries of the late Andrei Sakharov, the Soviet dissident for whom the prize is named.
They continue to lead the fight for democracy and human rights in Russia.
The Sakharov Prize has been awarded since 1988, and previous winners include Nelson Mandela, a former South African president, Xanana Gusmao, leader of East Timorese resistance, and Oswaldo Paya, a Cuban dissident.