Andrei Lugovoi, the main suspect in the radiation poisoning murder of Kremlin critic Alexander Litvinenko, is set to be elected to the Russian parliament.
Andrei Lugovoi has denied poisoning Alexander Litvinenko
Entering the Duma would bring immunity from prosecution in Russia.
The Crown Prosecution Service has said it has enough evidence to charge him with the murder of the ex-KGB agent, but he has protested his innocence.
With nearly 98% of ballots counted, Vladimir Putin's United Russia had 64.1% of Sunday's vote.
However, foreign observers have said that the parliamentary election was "not fair".
The statement was made by a joint observer team from Organisation for Security and Co-operation in Europe (OSCE) and the Council of Europe.
Following Mr Litvinenko's death in November 2006, it emerged that he had been given a massive dose of the radioactive substance polonium-210.
Mr Lugovoi, a former KGB officer, had tea with Mr Litvinenko at London's Millennium Mayfair Hotel on the day he fell ill.
Investigators suspect that a phial of polonium-210 could have been tipped into Mr Litvinenko's tea.
Traces of the substance were also found in a string of places Mr Lugovoi visited in London.
Mr Lugovoi has repeatedly denied any wrongdoing, suggesting that someone has been trying to frame him.
Alexander Litvinenko was poisoned with polonium-210
He underwent medical checks in hospital after traces of polonium-210 were reportedly found in his body.
He has also been questioned by Russian and British detectives as a witness.
British police tried, unsuccessfully, to extradite Mr Lugovoi.
In May the CPS announced it had enough evidence to charge him with murder, and requested his extradition to Britain to stand trial, but Russian prosecutors refused on the grounds that it was "against the Russian constitution".
Subsequently, Foreign Secretary David Miliband announced in July the expulsion of four Russian diplomats without revealing whether they were spies or not.
Russia responded by expelling four Britons from the embassy in Moscow.
Since the summer relations have not improved, although trade ties continue to flourish between the UK and Russia.
And Mr Lugovoi has made counter-accusations of "dirty tricks" by Britain's MI6, even suggesting it had a hand in Mr Litvinenko's murder.