Officers investigating the death of ex-spy Alexander Litvinenko will "follow the evidence wherever it goes", Home Secretary John Reid has said.
Mr Litvinenko died on 23 November in a London hospital
However, Russian Foreign Minister Sergey Lavrov warned that speculation over Mr Litvinenko's death was harming relations between Russia and the UK.
The comments came as UK police arrived in Moscow to pursue their inquiries.
The British Embassy in Moscow confirmed that one of its rooms would be tested for radiation as a precaution.
Former KGB bodyguard Andrei Lugovoi - who met former KGB agent Mr Litvinenko in London on 1 November - the day he fell ill - visited the embassy building in Russia last week to deny any involvement in the poisoning.
The Parkes Hotel in Knightsbridge - where Mr Lugovoi reportedly said he had stayed - and an office in Cavendish Place are the latest London locations being examined over the poisoning.
Earlier the Health Protection Agency (HPA) carried out tests at the Best Western Hotel in Shaftesbury Avenue, London, but found nothing of concern to public health.
"This investigation will proceed as normal, whatever the diplomatic or... wider considerations," Mr Reid said.
Speaking in Brussels at European Union talks, Mr Reid said that Foreign Secretary Margaret Beckett has "made plain to her Russian colleagues that we are asking them to give us all the support and information that they can".
The Kremlin has given assurances that support and information would be forthcoming, the home secretary added.
Mr Reid has also sought to reassure EU ministers over the health threat posed by the ex-spy's poisoning.
In Russia, foreign minister Mr Lavrov said Kremlin officials should not be involved in the British police inquiry.
"If the British have questions, then they should be sent via the law enforcement agencies between which there are contacts," he said.
He added the death of Mr Litvinenko, who was found to have traces of radioactive polonium-210 in his body, should not be politicised.
"The only thing that we are talking about today is the need to avoid politicising this issue, this tragedy.
"We are talking about the need to avoid speculations on this subject."
Speculation has been rife over the motives behind Mr Litvinenko's suspected poisoning.
Friends believe he was targeted because of his fierce criticism of the Putin government, but the Kremlin has dismissed suggestions it was involved in any way as "sheer nonsense".
Meanwhile, Mario Scaramella - an Italian contact of Mr Litvinenko's - is still being observed by doctors after testing positive for polonium-210.
However, doctors say Mr Scaramella, who met Mr Litvinenko the day the former KGB agent fell ill, remains well.
The BBC's Daniel Sandford said it was understood nine officers from the Metropolitan Police's counter-terrorism command could travel to Russia.
Mario Scaramella met Mr Litvinenko the day he fell ill
The specialist unit - launched in October to meet terrorist threats - is heading the investigation into Mr Litvinenko's poisoning.
Shadow home secretary David Davis welcomed news that the investigation was expanding.
He told BBC One's The Politics Show on Sunday: "I think it's a good thing, I think it's very important that no channel is left unpursued, that this investigation goes right to its limit wherever that may be and that limit should not be a diplomatic limit, it should be the limit of the evidence."
The Health Protection Agency said just over 3,000 people had called the NHS Direct line since the radiation scare, with 179 being followed up for further investigation.
Twenty-seven people were referred as a precaution to a specialist outpatient clinic for radiological exposure assessment.
A total of 70 urine samples, mainly from medical staff and ambulance workers, have been tested and found negative.