"It is important to stress that we have reached no conclusions as to the means employed, the motive or the identity of those who might be responsible for Litvinenko's death," the statement said.
It added that the inquiry was still in its early stages and that the police were not prepared to comment on "speculative reports" in the media.
Meanwhile, the foreign office in London confirmed that traces of radiation had been found at Britain's Moscow embassy.
"Expert teams concluded their precautionary checks in the embassy. They found no danger to public health," a spokesman said.
"This is not surprising, just look in history and you can find many cases such as Litvinenko's"
Z F Khan, Paris, France
Send us your views
"Small traces of radiation were found but below levels at which it becomes a risk to health and the embassy is working as normal."
Traces of radiation have been found at 12 locations around London.
Litvinenko fell ill on November 1 and died on November 23 in a central London hospital. Unexplained large amounts of the radioactive isotope polonium 210 were discovered in his urine.
The death has triggered a large-scale international investigation, meetings of the British government's top security cabinet and appeals for Russia to provide assistance to the inquiry.
In his deathbed statement, Litvinenko blamed Vladimir Putin, the Russian president's government, for his death.
The dissident was to be buried in a Muslim ceremony in or near London on Friday.
British investigators were in Moscow probing the death and met a witness in the case on Wednesday amid signs of discord with Russian prosecutors in the inquiry.