Prosecutor-General Yuri Chaika also insisted that the radioactive element used to poison the former spy could not have come from Russia.
In what is likely to be seen as a setback for Scotland Yard's investigation into Mr Litvinenko's death, Mr Chaika said it would be "impossible" for British investigators in Moscow to arrest Russian citizens in connection with the case.
Any Russian citizens suspected of involvement would be tried in Russia, he said.
His words contrasted with those of Prime Minister Tony Blair who insisted no political or diplomatic barrier would be allowed to stand in the way of the British investigation into Mr Litvinenko's death.
Home Secretary John Reid also insisted yesterday that politics would not hinder the inquiry and said the Russian authorities had promised their full support.
Mr Chaika did say that as part of their cooperation with British police, Russian prosecutors would question Andrei Lugovoi, a key witness in the inquiry.
Mr Lugovoi, a businessman and former KGB officer, met Mr Litvinenko in a Mayfair hotel on the day he was allegedly poisoned.
It is unclear what access the team of nine Scotland Yard officers currently in Russia will be given to that process.
In a press conference today, Mr Chaika said the polonium 210 found in Mr Litvinenko's system could not have originated in Russia.
He also said Russia would not extradite possible suspects to Britain.
"If they want to arrest them it would be impossible, they are citizens of Russia and the Russian constitution makes that impossible," Mr Chaika said.
A Home Office spokesman confirmed that the Russian legal system did not permit the extradition of its own citizens.
Nobody has been extradited from Britain to Russia for 15 years.
The Foreign Office and Scotland Yard refused to comment on Mr Chaika's comments.
The arrival of British police officers in Russian marks the start of a crucial period for the police investigation and for Anglo-Russian political relations.
Russia's Foreign Minister, Sergey Lavrov, has already warned that persistent suggestions of Russian involvement could harm diplomatic relations.
It emerged today that Mr Litvinenko's funeral would be held this week, however the exact day is still unclear.
The family have been given dispensation by the coroner to proceed with the burial following last week's post mortem examination.
Radiation tests are being carried out today on one room at the British Embassy in Moscow by experts from the UK Government Decontamination Service.
It is said to be where Mr Lugovoi gave a statement about his meeting with Mr Litvinenko at the Millennium Hotel to Britain's deputy ambassador.
The Health Protection Agency (HPA) confirmed last night that two new addresses in London were also being examined for traces of radiation.
They include the luxurious Parkes Hotel in Knightsbridge, where Mr Lugovoi reportedly stayed during a previous visit to London.
Mr Lugovoi is reported to have been tested for radiation contamination in Russia, but found to be clear.
However, Russia's Kommersant daily today quoted the businessman's lawyer, Andrei Romashov, as saying he had checked into a hospital for further tests.
Officers from Scotland Yard's counter terrorism unit were hoping to interview several potential witnesses in Russia, including Mr Lugovoi and possibly his associates Dmitry Kovtun and Vyaceslav Sokolenko.
The force is awaiting the result of the post-mortem on Mr Litvinenko, which was carried out on Friday. That is likely to be released sometime this week. At the moment, it is being treated as a suspicious death.
A local Russian police force is escorting the British detectives during their trip, which could last several days or even weeks.
Scotland Yard has also been urged to contact the jailed former Russian intelligence officer Mikhail Trepashkin, who apparently wrote a letter which purported to show the existence of a secret squad set up to target Mr Litvinenko.
However, it has been reported that the British police officers will not be allowed to see Trepashkin because he was convicted of divulging state secrets and cannot meet representatives of foreign governments.
The other man known to have met Mr Litvinenko on the day he was poisoned, the Italian academic Mario Scaramella, has also tested positive for polonium 210.
University College Hospital, which is treating Mr Scaramella, said today he remained "well" and that his condition was unchanged from yesterday.
It has been claimed he could be released from hospital later today.
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