Mr Miliband is due to meet his Russian counterpart again on Monday
David Miliband has met his Russian counterpart in Moscow on the first visit to the country in five years by a British foreign secretary.
Relations between the UK and the Kremlin reached a low after the murder in London of Russian emigre Alexander Litvinenko in November 2006.
Mr Miliband met Sergei Lavrov for dinner and informal talks, ahead of a further meeting on Monday.
Discussions are 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.
Bridget Kendall, BBC diplomatic correspondent
Not since July 2004 has a British Foreign Secretary been to Moscow - an extraordinarily long time, given the volume of trade between the two countries and the global problems they are both concerned about.
But relations were plunged into a freeze following the tit for tat diplomatic expulsions that followed the Litvenenko murder.
On the eve of Mr Miliband's arrival in Moscow the Russian ambassador to London was still blaming Britain for an "anachronistic" attitude and "artificial barriers" which stood in the way of improved relations.
Both countries agree they need to work together. But neither side seem to think they'll find a way past their deep seated disagreements.
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 does not always "see eye to eye" with Russia but acknowledged it is 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.
Relations between Britain and Russia took a turn for the worse after former Russian security agent Mr Litvinenko was poisoned.
Moscow refused UK requests to extradite chief suspect Andrei Lugovoi and several tit-for-tat diplomatic expulsions took place as the row rumbled on.
The situation worsened further when Moscow ordered the closure of British Council offices due to alleged tax irregularities.
There have also been tensions over spying claims and a struggle over BP's interests in Russia.
Meanwhile, a group of MPs has urged Mr Miliband to raise human rights issues with Mr Lavrov.
A letter signed by MPs including Labour's Tom Watson, Tory Julie Kirkbride and Liberal Democrat Julia Goldsworthy, highlights concerns over the fraud trial of former oligarch Mikhail Khodorkovsky, which his supporters claim is politically motivated.
"It is clear that the UK must raise concerns regarding Russia's lack of respect for human rights, property rights and rule of law; and challenge the use of national energy providers as an aggressive foreign policy tool which isolates Russia from the rest of the international community," they say.
The Foreign Office said Mr Miliband would not be attending Mr Khodorkovsky's trial.
"Whilst the legal processes in every country are a matter for that country, we always make clear the importance of human rights, the rule of law and judicial processes that are seen to be fair and transparent," a spokesperson said.
The spokesperson added that the UK had an "annual bilateral dialogue with Russia to discuss human rights as well as the opportunity to raise concerns through the EU/Russia human rights talks".
Mr Miliband's visit comes as Downing Street plays down a story in the Sunday Times which says Gordon Brown is backing him to be the EU foreign affairs chief.
A source said David Miliband has made it clear that he was not a candidate and not available.