DHAKA (Reuters) - Bangladeshis on Sunday paid tribute to an American critic of religious extremism killed in Dhaka, in the latest of a series of attacks on writers who support free thinking values in the Muslim-majority nation.

Avijit Roy, a U.S. citizen of Bangladeshi origin, was hacked to death by machete-wielding assailants on Thursday after a book fair, sparking widespread condemnation from home and abroad.

His wife and fellow blogger Rafida Ahmed suffered head injuries and lost a finger and remains in hospital in a serious condition.

The attack comes amid a crackdown on hardline Islamist groups, which have increased activities in recent years in the South Asian nation of 160 million people.

No arrest has been made.

People from all walks gathered with flowers at the Dhaka University premises on Sunday to pay their respect to Avijit, who came to his native city in mid-February and was due to go back to the United States.

"Free thinking in Bangladesh is become a great danger, all the free thinkers are at great risk," writer Shahriar Kabir said.

"We want to know why the government failed to ensure the safety of him, despite knowing that he had been facing threats from the Islamist radicals."

Family members donated the body of Avijit to the Dhaka Medical College Hospital for medical research to show respect for his wish.

Roy's family said Islamist radicals had been threatening him in recent weeks because he maintained a blog, "Mukto-mona," or "Freemind," that highlighted humanist and rationalist ideas and condemned religious extremism.

U.S. State Department spokeswoman Jen Psaki called it "a shocking act of violence" that was "horrific in its brutality and cowardice" and said the United States was ready to assist the investigation.

U.N. spokesman Stephane Dujarric condemned the attack, and called for a swift and thorough investigation.

Media group Reporters Without Borders rated Bangladesh 146th among 180 countries in a ranking of press freedom last year.

In 2013, religious extremists targeted several secular bloggers who had demanded capital punishment for Islamist leaders convicted of war crimes during Bangladesh's war for independence.

Blogger Ahmed Rajib Haider was killed that year in a similar attack near his home in Dhaka after he led one such protest demanding capital punishment.

In 2004, Humayun Azad, a secular writer and professor at Dhaka University, was also attacked by militants while returning home from a Dhaka book fair. He later died in Germany while undergoing treatment.

(Reporting by Ruma Paul; Editing by Michael Perry)