It called on the Bangladesh authorities to send “a strong message... that killings will not be tolerated”.
Niloy, who wrote against communalism and fundamentalism, was hacked to death at his house in front of his wife on Friday by several youths.
“This spate of savage killings must end here,” the Amnesty statement quoted David Griffiths, its South Asia Research Director, as saying.
He said the killings of the secular bloggers were designed to instil fears on free speech.
“This is unacceptable,” Griffiths added.
He said Bangladesh has an “urgent duty to make clear that no more attacks like this will be tolerated”.
The statement called for bringing the perpetrators to justice “without recourse to the death penalty”.
Meanwhile, Joyce Anelay, UK’s Minister of State at the Foreign & Commonwealth Office, also condemned Niloy’s killing.
“Appalled at murder of blogger Niloy Neel. Perpetrators must be brought to justice and free speech in #Bangladesh defended robustly,” she tweeted.