Liberal Democrat ministers will shun the Winter Olympics in Sochi in protest over "regressive" anti-gay laws but Tories will attend the opening ceremony.
Deputy Prime Minister Nick Clegg said there was outrage across his party over Russia's human rights record and insisted governments "shouldn't in any way endorse or directly, or indirectly" Moscow's actions.
But Prime Minister David Cameron believes it is right for Culture Secretary Maria Miller to represent Britain at the start of the games tonight, Downing Street said.
"The Government, including the Prime Minister, has and will continue to make clear our views about the importance of tolerance, respect for individual rights," the PM's official spokesman said.
"The Prime Minister has, and will continue, to raise that with president Putin as will all Government ministers."
Mrs Miller intends to raise human rights issues during her visit, the spokesman added.
"The Prime Minister does think it's right that the Secretary of State is at the opening ceremony, yes."
Mr Clegg said he was "appalled" by president Putin's decision to introduce a law banning the "promotion" of homosexuality and said he hopes gay men and women travelling to Russia feel able to speak out - despite Foreign Office advice warning that visitors could face arrest, fines and deportation.
He told LBC 97.3: " It's just the most regressive law imaginable, it has a very chilling effect, intimidating effect, on many people in the lesbian, bi-sexual, gay community in Russia and elsewhere.
"It sends out an appalling signal. I am not in favour of sports boycotts, in fact I am a big fan of winter sports. I will be cheering our athletes as much as anyone else when watching the Sochi games, now and in the coming days. But, you know, does that mean I am going to go there?
"No, I am not going to go there and I certainly wouldn't want any Liberal Democrat minister to go there given the strength of feeling in my party and I feel this very strongly as well, that what Russia has done, on that legislation, is just plain wrong."
He added: "Well we can make it painfully clear that whilst we are not suggesting that somehow we should end the athletic spectacle that is the Winter Olympics, I am not in favour of athletic boycotts, we can certainly make it clear, as politicians, and as governments. I certainly feel this very strongly, my party does as well, that what the Russian government does, has done, is wrong and we shouldn't in any way endorse or directly, or indirectly, give any succour to what they have done."
Mr Clegg said he hoped Britons attending the games would feel " emboldened to speak out against a very regressive piece of legislation".
Told they might get arrested, he replied: "W ell, Putin has said they are welcome but I hope he means what he says when he said that because the legislation that his government has passed points in exactly the opposite direction, it is totally out of step with the need to provide everybody from whatever sexuality, whatever orientation, the right to freedom of expression and to proper dignity in whatever society, including in Russia."