It also called for a “prompt” investigation to bring perpetrators to justice.
The EU reiterated its “strong attachment to freedom of expression which constitutes an essential element of a democratic society”.
“The EU Ambassador expresses his condolences to Mr Roy's family,” said an EU statement on Facebook on Friday.
Unidentified assailants hacked Avijit to death and seriously injured his blogger wife Rafida Ahmed Bonya on Dhaka University campus on Thursday night.
His father, professor Ajay Roy, filed a case of murder with Shahbagh police on Friday and said extremists were behind the murder and “Jamaat(-e-Islami) has backed them”.
The case did not name anyone.
Islamist zealots had been threatening Avijit, a bioengineer and a naturalised US citizen, for his active campaign against Islamist radicals.
He was a regular bdnews24.com columnist and the founder of the popular blog, Mukto-Mona.
British High Commission in Dhaka Robert Gibson earlier expressed his shock over the killing in a tweet.