The Prime Minister said last week that he believes it would be "better to challenge prejudice as we attend" the Winter Olympics in Russia, as calls from athletes to boycott it over its anti-gay laws continue.
Russia's pole vault world champion Yelena Isinbayeva defended the country's controversial new law, however, British heptathlete Louise Hazel said the Russian's position as ambassador for the Youth Olympics was now "ridiculous".
In response to a letter Stephen Fry wrote urging him to back the boycott, David Cameron wrote on Twitter: "I share your deep concern about the abuse of gay people in Russia...However, I believe we can better challenge prejudice as we attend, rather than boycotting the Winter Olympics".
Broadcaster Stephen Fry suggested athletes at the Winter Olympics in Sochi should create a crossed-arm "symbol" during the Games to show support for gay people in Russia.
"All athletes in the games should find a symbol - during their performance or at the end of it, and certainly on the medial podium - to show they are thinking of the gay people of Russia," Fry told BBC News at an LGBT rally in central London.
He suggested athletes could adpot a "simple" symbol of crossing their arms while holding their shoulders.
"It would just take some of the sweetness of victory out of Vladmir Putin's mouth," said Fry.
Stephen Fry said he believes the Winter Olympics in Sochi will not be moved or boycotted after David Cameron said he did not support a boycott.
"My feeling now is that it isn't going to change," Fry told BBC News.
The broadcaster said his call to move the Games to another country was "probably not realistic in terms of being likely".
He added: "But it's realistic to call for it, and if it makes anybody look online and see how gays are being treated in Russia - it's horrifying and it's getting worse."
Stephen Fry said the Prime Minister "may be right" after he ruled out boycotting the 2014 Winter Olympics in Russia, but asked, "Is there nothing we can do?"
After David Cameron said it was "better to challenge prejudice as we attend" the event in Sochi, Fry wrote on Twitter:
.@david_cameron PM, you may be right. Would that have been true in 1936? But is there nothing we can DO? Putin grow and grows in confidence
Lots of people popping down to Whitehall to make their feelings known. What to wear, what to wear?
David Cameron said he believes it would be "better to challenge prejudice as we attend, rather than boycotting the Winter Olympics" in Russia.
In response to a letter Stephen Fry wrote urging him to back the boycott, the Prime Minister wrote on Twitter:
1/2 Thank you for your note @stephenfry. I share your deep concern about the abuse of gay people in Russia...
New laws in Russia banning the promotion of "non-traditional relationships" have raised questions about the country's suitability to host the 2014 Winter Olympics.
Pink News publisher Benjamin Cohen explains what the laws could mean in practice, and why the International Olympic Committee may be prompted to look again at its choice of host city.
The president of the International Olympic Committee has said he is waiting for clarification from the Russian government on the anti-gay law that is overshadowing preparations for the Winter Games in Sochi.
"We are waiting for the clarifications before having the final judgement," Jacques Rogge told reporters.
"The Olympic charter is clear," Rogge said. "A sport is a human right and it should be available to all, regardless of race, sex or sexual orientation."
A spokesman for the British Olympic Association has said his organisation believes a boycott of the Winter Olympics in Sochi would serve only to "penalise athletes".
Darryl Seibel told ITV News that Olympic bosses are monitoring the situation in Russia closely and that the safety of athletes is a top priority.
A petition calling on the International Olympic Committee (IOC) to relocate the 2014 Winter Games away from Russia has garnered almost 130,000 signatures.
Petitioners want the Games to be taken away from Sochi because of laws in Russia which they say discriminate against LGBT people. They suggest relocating to Vancouver in Canada, which hosted the Games in 2010.
A Government spokeswoman said:
We remain greatly concerned about the growing restrictions on LGBT freedoms in Russia and have repeatedly raised our concerns, including at the 2013 UK-Russia Human Rights dialogue in May.
The Prime Minister outlined our concerns with President Putin during a meeting in Downing Street in June ahead of the G8 Summit.
We are working closely with the IOC and the BOA to ensure that the Games take place in the spirit of the Olympic Charter and are free from discrimination.