Peter Tatchell, director of the Peter Tatchell Foundation human rights organisation, has appealed to Alex Salmond to express concern at the "persecution of lesbian, gay, bisexual, transgender and inter-sex (LGBTI) people in 42 of the 53 Commonwealth member states".
Mr Tatchell said: "We urge him to appeal to all participating countries to adhere to Article 7 of the Commonwealth Games Federation constitution, which prohibits all discrimination."
He said countries that "perpetuate discrimination in access to sports facilities, training camps or team selection" should be barred from participating in the Commonwealth Games.
"If they are not prepared to abide by Article 7 they have no right to come to Glasgow or future Commonwealth Games," he said.
Mr Tatchell also urged the Commonwealth Games organisers to take a tougher line against countries that discriminate and has written to Glasgow 2014 chief executive David Grevemberg.
Mr Tatchell added: "80% of Commonwealth countries discriminate against LGBTI people.
"The intensity of homophobia in these countries is so great that it is very unlikely that they would select an LGBTI athlete to compete in Glasgow.
"I can't imagine homophobic states like Uganda, Brunei or Nigeria selecting an LGBTI athlete. They are more likely to jail them than send them to Glasgow.
"Although the Glasgow 2014 administrators are commendably committed to equality and diversity, they have disappointingly not agreed to the Peter Tatchell Foundation's request to require all participating nations to sign a pledge to uphold Article 7."
The appeal comes as Scotland's Cabinet Secretary for Commonwealth Games Shona Robison opened Pride House in Glasgow.
The venue is said to demonstrate a "commitment to lesbian, gay, bisexual, transgender and inter-sex equality on the international stage" and plays host to a range of sports, discussion, cultural and arts events aimed at breaking down the barriers which discourage LGBTI people from participating in sports.
Led by Leap Sports Scotland, Pride House will also provide more information and advice about the wider events programme in 2014 for LGBTI visitors and act as a meeting space for the community.
The Scottish Government is providing almost £25,000 to support Pride House and its programme of more than 70 events during the Games.
Ms Robison said: "Major sporting events like the Commonwealth Games bring together people from all walks of life and are an opportunity to celebrate diversity.
"The events and activities at Pride House are a crucial part of this work and will help to deliver a successful, secure and safe Games that everyone can attend without fear of prejudice or discrimination.
"By increasing the visibility of LGBTI people in sport, either through LGBTI-specific sports groups or addressing discrimination where it exists in mainstream sports, we are working towards making sport more inclusive to all.
"I'm confident that equality and human rights initiatives around the Games, such as Pride House, will provide a warm welcome to members of the LGBTI community and will create a legacy for the future."
Hugh Torrance, chair of Leap Sports Scotland, said: "International sporting events such as the Commonwealth Games give us an excellent opportunity to consider equality in sports and wider human rights issues, and I'm delighted that Pride House Glasgow creates a space where this can happen.
"The Pride House Glasgow programme has been designed to be inviting to all ages and we look forward to seeing athletes, visiting delegations, officials and visitors using the space alongside the LGBT community of Scotland."
Mr Salmond said Scotland demonstrates its commitment to LGBT rights through its actions.
He told an audience of international media representatives in Glasgow: "Our sports minister opened Pride Glasgow today, which will have its message of equality and non-discrimination displayed, not just in the opening of one centre in Pride Glasgow, but the 70 events which are taking place as part of that initiative in Glasgow over the course of the Games.
"In St Andrew's House (government building in Edinburgh) we fly the rainbow flag, sometimes called the pride flag internationally, for the course of the Games.
"So, we demonstrate our commitment and we provide an exemplar in terms of what we believe in.
"That's what I think is the best way to state our commitment, it's by what we do and how we act and what we display and what we advocate."
Mr Salmond spoke after being asked for his response to those human-rights organisations urging him to condemn the Commonwealth countries where homosexuality is a criminal offence.
Elsewhere, the Speaker of the House of Commons, John Bercow, voiced his concern about the treatment of LGBT people in some parts of the Commonwealth.
He said: "Sadly, there might be world-class athletes who will not be able to compete in the Games, as they will have been discriminated against on the basis of their sexuality; shamefully, it is estimated that four out of every five countries in the Commonwealth criminalise homosexuality.
"Surely, it is time for the Commonwealth to do more to support lesbian, gay, transsexual and bisexual people, to ensure they are not discriminated against, no matter where they live?"