The trip is Mr Hague’s first to Moscow as foreign secretary William Hague will hold meetings later with Russian President Dmitry Medvedev in his first trip to Moscow as foreign secretary.
Mr Hague has played down expectations ahead of the visit, but said “the door was open to better relations”.
Relations between the two countries have been strained over the murder of ex-spy Alexander Litvinenko in London in November 2006.
Britain’s 2007 request for the extradition of a suspect still stands.
UK investigators suspect former KGB agent Andrei Lugovoi of the murder, but he has always denied any involvement in the poisoning of Mr Litvinenko with the radioactive substance polonium-210.
In May 2007, the Crown Prosecution Service formally submitted an extradition request to Moscow for Mr Lugovoi to stand trial in Britain.
Russia has refused to co-operate, saying it would be against its constitution to do so.
Ahead of his talks with Mr Medvedev and Foreign Minister Sergei Lavrov, Mr Hague told the BBC that better, businesslike relations were desirable, but that did not mean Britain was setting aside differences with Russia over the Litvinenko murder.
“It’s not a problem that can be ignored.”
William Hague Foreign Secretary
Russia has signalled it hopes Mr Hague’s visit will help put irritants aside, and called on Mr Hague to take concrete steps towards it.
Mr Hague, though, insisted it was not yet time to turn a corner.
“[The Litvinenko murder] remains a major problem in bilateral relations and I don’t think that problem is going to go away.
“It’s not going to be set aside, it’s not going to be put behind us, it is something we will have to continue to discuss with Russia.
“So, it’s not a problem that can be ignored but I think while we discuss that with Russia there are other things we can be doing.”
However, Mr Hague does want to explore the potential for collaborative projects that could help businesses and jobs in Britain.
No “reset button” – as the US has described its hopes for its own relations with Russia – then, or a fresh start, but a small step to improve relations, says the BBC diplomatic correspondent Bridget Kendall.
Afghanistan, Iran’s nuclear programme, and the Middle East peace process are also expected to be on the agenda.
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