"This would contradict the Russian Constitution," Yury Chaika said.
British investigators arrived Monday to interview people who met with Alexander Litvinenko, a Russian security service defector, around the time of his reported radioactive poisoning in early November.
Speaking at a news conference, Chaika also said Russian prosecutors would conduct questioning for their British colleagues in Russia, but that they would not be able to take other investigative action related to crimes perpetrated on foreign territory.
Chaika also reaffirmed the Russian side's willingness to provide other assistance in the investigation into the poisoning of Litvinenko, an outspoken Kremlin opponent who died November 23.
Moscow has denied involvement in the death of the former agent, and suggested his deathbed letter, in which he accused the Russian president of ordering his murder as revenge for defection in 2000, was a fake.
British newspapers earlier reported that in Russia, Scotland Yard detectives were to question a businessman and former KGB and FSB colleague, Andrei Lugovoi, businessmen Dmitry Kovtun and Vyacheslav Sokolenko, and several other people.
But the chief prosecutor said Lugovoi, a former bodyguard for fugitive Russian oligarch Boris Berezovsky, and well acquainted with Berezovsky's friend Litvinenko, was in hospital and might only be questioned there if doctors gave their permission.
"This will depend on the doctors. If they allow it, Lugovoi will be questioned."
In late November, Lugovoi visited the British Embassy in Moscow, saying he was willing to help Scotland Yard investigate his former colleague's death.
Another security officer seeking a meeting with British investigators in Russia has been denied his request on the grounds that he is in prison on treason charges and is therefore not allowed to contact foreign security services.
Mikhail Trepashkin, serving a four-year sentence for divulging state secrets, claims he had warned Litvinenko of planned attempts on his life, and has important evidence to share with investigators.
His defense lawyer dismissed the decision as hindering the investigation. But Chaika said Monday Scotland Yard had not requested a meeting with Trepashkin.
"Trepashkin was not mentioned in the assistance request... Today half of all prisoners [in Russia] can claim to have this or that information." he said.
The chief prosecutor also dismissed suggestions that radioactive isotope polonium-210, found in Litvinenko's body, had been smuggled from Russia as impossible, and denied reports naming certain Russian factories that had allegedly produced the substance.
"It was never produced there, this is disinformation," he said, adding it was impossible to transport such a large dose of polonium as that used to poison Litvinenko, across the border.
He said it was up to experts in Britain, where the case was opened, to determine the origin of the radioactive isotope.
Po-210 radiation was also found at a dozen sites in London and on British Airways aircraft that had flown the London-Moscow route.