At a press briefing at the UN headquarters on Friday (local time), Stéphane Dujarric, spokesperson for the secretary general, hoped the perpetrators would be quickly brought to justice.
Roy, who worked at a US software company, and his wife were attacked near Dhaka University’s TSC on Thursday night.
He was the founder of ‘Mukto-Mona’ blog and used to write against communalism and religious superstitions.
Fundamentalists had threatened him on several occasions for his writings.
His father Prof Ajay Roy, who teaches at Dhaka University, has blamed militants for the attack.
Dujarric said: “On the attack of the blogger, we spoke to our human rights colleagues who obviously condemned the attack and expressed the hope that the perpetrators will be quickly brought to justice through the due process of law.
“It's obviously very important that the space for freedom of expression in civil society be upheld in Bangladesh.”
Thursday’s attack was similar to the one on renowned writer Humayun Azad in 2004.
Police are yet to make headway in Roy’s case.
The US has offered assistance with investigation.