David Miliband has insisted that festering disputes between the UK and Russia over issues such as the Alexander Litvinenko murder would not prevent closer co-operation.
Speaking as he became the first British foreign secretary to visit Moscow for five years, Mr Miliband welcomed increasing "common ground" between the two countries.
But he said the Government would not "paper over" differences as it seeks to thaw relations.
"The cultural and business links that are growing, I think, are testimony to the importance of the UK-Russia relationship," Mr Miliband told a press conference.
"That is reflected now at governmental level - not just on issues of the economy and foreign policy, but also on energy, climate change and other issues."
He continued: "We don't paper over our differences but we don't allow them to block co-operation".
Mr Miliband branded the 2006 murder in London of former Russian spy Litvinenko "horrific".
Moscow has refused requests to extradite Scotland Yard's chief suspect, Andrei Lugovoi, sparking tit-for-tat diplomatic expulsions.
Mr Miliband said: "We can continue to be absolutely open about the importance that we attach to (these issues) and we don't trade them off. Instead, we say there are other areas where there is more common ground and we are determined to work together."
Russian foreign minister Sergei Lavrov said their talks had been "positive and productive", but insisted the Russian constitution forbade extradition of its citizens. He added: "The demands that we basically change our constitution are absolutely unrealistic."
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