Relations between the UK and the Kremlin reached a low after the murder in London of Russian emigre Alexander Litvinenko in November 2006.
But Mr Miliband insisted the UK’s continued demand for the extradition of the main suspect in the killing would not block co-operation on other issues.
The foreign secretary said the talks had been “substantive and productive” and marked by “mutual respect”.
He added that, although there were differences between the two countries, there had been a “genuine search for common ground and common action”.
Mr Miliband told reporters: “The cultural and business links that are growing, I think, are testimony to the importance of the UK-Russia relationship.
“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 had met Sergei Lavrov for dinner and informal talks ahead of the meeting.
Discussions were expected to cover Iran, the Middle East and Afghanistan.
According to BBC diplomatic correspondent Bridget Kendall, a senior diplomat has indicated the main focus will be on issues where Russia’s collaboration is needed internationally – over Afghanistan, and over the question of Iran’s nuclear programme.
The aim, said the diplomat, was to be clearer about Russia’s position on Iran, and whether if current negotiations with Tehran failed, Russia would be prepared to adopt a tougher position.
The last British foreign secretary to visit Russia was Jack Straw in 2004. But Prime Minister Gordon Brown has spoken frequently with Russian president Dmitry Medvedev at international summits.
Ahead of his arrival, Mr Miliband said the UK still did not always “see eye to eye” with Russia but acknowledged it was a world power and an important trading partner.
Writing on his blog, Mr Miliband said: “We share the same global challenges and it is important that we work on them together.
“The wealth of people-to-people contacts and the dynamic business links which have grown between Britain and Russia over the last 20 years make political engagement all the more important.”
The Foreign Office said Mr Miliband would meet a range of politicians, business leaders and representatives of civil society before returning home on Tuesday.