Nick Clegg called for greater protection for the rights of lesbian, gay, bisexual and transgender (LGBT) people around the globe on a visit to the city's newly opened Pride House.
He met campaigners, athletes and volunteers at the centre, which has been set up to promote diversity at the Games and within the Commonwealth.
With just hours to go until the Games begin, campaigners have been highlighting inequality in many of the participating countries.
Mr Clegg said: "The Commonwealth core values and principles which all Commonwealth countries sign up to are clear.
"They say that 'We are committed to equality and respect for the protection and promotion of civil, political, economic, social and cultural rights'.
"Yet almost 80% of Commonwealth countries (42 out of 53 countries) that are represented here in Glasgow this week criminalise homosexuality in some way."
He celebrated recent progress towards equality in the UK, including last year's landmark equal marriage reform, but added that a "huge amount" remains to be done globally.
Mr Clegg said: "As we celebrate the bravery of Olympians who have come out - Tom Daley, Ian Thorpe or Nicola Adams for example - some countries are taking backward steps; putting their LGBT Olympians so far back in the closet that they can't ever imagine their day in the open.
"We can't dictate how other nations behave but we can promote the principles we believe in - of a fair and open society both in the UK and abroad.
"The message is clear: LGBT rights are human rights. So we need LGBT protections to be a part of anti-discrimination laws everywhere."
Meanwhile the lesbian, gay, bisexual, transgender and intersex (LGBTI) Human Rights in the Commonwealth conference published a "call to action".
The conference, held earlier this month, was organised by the Glasgow Human Rights Network at the University of Glasgow, along with Equality Network, Kaleidoscope Trust and Pride Glasgow.
Its statement calls for equal rights for LGBTI citizens to be a "substantive agenda item" at the next Commonwealth Heads of Government Meeting in Malta in 2015.
Earlier this week Peter Tatchell, director of the Peter Tatchell Foundation human rights organisation, also spoke out against the persecution of LGBT people in Commonwealth countries.
He called on Commonwealth Games organisers to take a tougher line against countries that discriminate and urged Scottish First Minister Alex Salmond to voice his concern.
Mr Salmond said Scotland demonstrates its commitment to LGBT rights through its actions.
The Scottish Government is providing almost £25,000 to support Pride House and its programme of more than 70 events during the Games.
Speaking later Mr Clegg said: "I hope that through places like Pride House we can gently but firmly, respectfully but consistently urge fellow Commonwealth countries to not only pay lip service to the values of the Commonwealth but also honour those values that include respecting everyone in society, regardless of their faith, background and sexuality."
Asked why today was a good opportunity to highlight the issue he said: "The launch of the Commonwealth Games is a joyous celebration of sporting excellence and that's why I think this is a good moment to say we should not brush under the carpet some of the areas where Commonwealth countries have a lot more to do."
Asked whether the UK could put pressure on countries which discriminate against homosexuality he said: "Recently when there were measures taken to discriminate against homosexuality in Uganda we were very clear and outspoken in our condemnation of it but we can't run the domestic affairs of other countries. We can lead by example."