Human rights campaigner Peter Tatchell is calling on Prime Minister David Cameron to speak out against homophobia and declare his support for non-discrimination.
Mr Tatchell has previously written to the organisers of the Games, which start next Wednesday, urging them to ensure that all member countries competing in Glasgow pledge their commitment to Article 7 of the constitution of the Commonwealth Games Federation.
This states that "there shall be no discrimination against any country or person on any grounds whatsoever, including race, colour, gender, religion or politics".
In 42 of the 53 member countries of the Commonwealth homosexuality is a criminal offence, the Peter Tatchell Foundation said, with penalties of up to life imprisonment in at least seven member states and the death penalty in parts of northern Nigeria and rural Pakistan.
Mr Tatchell said: "Given the extreme homophobia and transphobia in most Commonwealth countries, it is very unlikely that most national selection committees would allow a lesbian, gay, bisexual, transgender or inter-sex (LGBTI) athlete to compete at Glasgow.
"David Cameron can help by making clear that such discrimination is incompatible with Commonwealth Games values and rules.
"We want the Prime Minister to give a lead and set a positive tone by publicly declaring that anti-LGBT persecution is a violation of the Commonwealth Charter and that LGBTI athletes will be welcome in Glasgow.
"We are asking him to state his support for Article 7 and to make it clear that no country should be permitted to discriminate with regard to who they select for the up-coming Games."
The rally at Downing Street has been organised by the African LGBTI Out and Proud Diamond Group, with the support of the Peter Tatchell Foundation and Rainbows Across Borders.
Campaigners are also urging LGBTI athletes at the Games to come out if it is safe for them to do so, and are calling on the government to grant asylum in the UK to LGBTI athletes and officials who fear persecution if they return to their home countries.
Edwin Sesange, co-ordinator of the African LGBTI Out and Proud Diamond Group, said: "The Commonwealth Games is a major international sporting event and a great opportunity for the Prime Minister speak out against anti-LGBTI persecution by 80% of Commonwealth member states.
"We want him to press the Glasgow 2014 organisers to make equality a key theme of the Games. This would be a unique, pioneering achievement; setting a non-discrimination standard for future Games organisers to follow."