The US ambassador to Bangladesh condemned the killing of Xulhaz Mannan, who also worked at the US embassy.
Another person was also injured when the attackers entered a Dhaka flat.
Since February last year suspected militants have killed several secular or atheist writers and members of religious minority groups.
The two men were murdered two days after a university teacher was hacked to death by suspected Islamist militants.
So-called Islamic State (IS) claimed responsibility - but the Bangladeshi government insists there is no IS presence in the country.
Lurching from secularism to sectarian terror?
Who is behind the Bangladesh killings?
"I am devastated by the brutal murder of Xulhaz Mannan and another young Bangladeshi," said US Ambassador Marcia Bernicat.
"We abhor this senseless act of violence and urge the government of Bangladesh in the strongest terms to apprehend the criminals behind these murders," she added.
BBC Bengali Service editor Sabir Mustafa said staff at Roopbaan, a magazine and activist group for the Lesbian, Gay, Bisexual and Transgender (LGBT) community that had not been condemned by the government and received some support from foreign embassies, had been careful to protect their identities but had not believed their lives were at risk.
Suspected extremists in Bangladesh are gaining a sense of security that they can carry out killings with impunity, he says.
A British photographer who knew Mr Mannan and the other victim, known as "Tonoy" and named in Bangladeshi media as Tanay Mojumdar, said they and other friends had set up Roopbaan with the aim of spreading tolerance.
Homosexuality is technically illegal in Bangladesh and remains a highly sensitive issue in society.
Both men were openly gay and believed that if more gay Bangladeshis came out then the country would have to accept them, the photographer, who asked not to be named, said.
They were also were behind the annual "Rainbow Rally", held on Bengali New Year, 14 April, since 2014. This year's rally was banned by police as part of widespread security measures.
"Both were extremely gentle, non-violent and aware that being openly gay and active in their work was a personal danger," the photographer said.
Their killings were likely to spread fear among Bangladesh's gay community, he said.
"Until a year ago the only threat to coming out was shame of the family and having to start a new life elsewhere in Bangladesh. Now it's one of danger," he said.
Meanwhile Bangladesh's best known blogger said he had received a death threat on Sunday.
Imran Sarker, who led major protests by secular activists in 2013 against Islamist leaders, said he had received a phone call warning that he would be killed "very soon".
Earlier this month, a Bangladeshi law student who had expressed secular views online died when he was hacked with machetes and then shot in Dhaka.
Last year, four prominent secular bloggers were also killed with machetes.
The four bloggers had all appeared on a list of 84 "atheist bloggers" drawn up by Islamic groups in 2013 and widely circulated.
There have also been attacks on members of religious minorities including Shia, Sufi and Ahmadi Muslims, Christians and Hindus.
Two foreigners - an Italian aid worker and a Japanese farmer - have also been killed.
Muslim-majority Bangladesh is officially secular but critics say the government has failed to properly address the attacks.
Bangladesh police say a top gay rights activist and editor at the country's only LGBT magazine is one of two people who have been hacked to death.