Police in Germany say they have found indications of radiation in two properties apparently used by a contact of murdered spy Alexander Litvinenko.
Mr Kovtun is reportedly being treated in Russia
Dmitry Kovtun, who met the former KGB agent on the day he fell ill, is being treated in hospital in Russia.
Police said traces of radiation were found at the Hamburg flat of his ex-wife and at her mother's home outside the city.
Officials in Moscow said Russian police may travel to Britain.
No radiation had been found at Mr Kovtun's own flat, which is in the same Hamburg apartment block, police said.
But the traces of radiation which were discovered in his ex-wife's Hamburg flat and the home of Mr Kovtun's former mother-in-law in the town of Haselau, west of Hamburg, could be a sign that a source of radiation had been there, they said.
Hamburg police said neither woman was a suspect in the investigation, but Mr Kovtun's 31-year-old ex-wife had been questioned by officers.
The apartment building was evacuated while police searched the flats, but officers said there was no danger to the public.
German police had previously stated their intention to examine Mr Kovtun's apartment in the city for traces of polonium-210, the radioactive substance found in murdered Mr Litvinenko's body.
It followed reports that Mr Kovtun had flown from Hamburg to London, where he met Mr Litvinenko last month.
Mr Kovtun is reportedly being treated in hospital for radiation poisoning.
The apartment block in the Ottensen district of the northern port city and the Haselau property are the latest in a series of buildings - most of them in London - to have been searched as part of inquiries into Mr Litvinenko's death.
Andrei Lugovoi has failed to meet investigators for questioning
The British murder inquiry is being run parallel to an investigation in Russia, but Moscow has said it will not extradite any suspects in the case to the UK.
A spokeswoman from the Russian Prosecutor General's Office has told the BBC that Moscow is considering sending a group of Russian police officers to Britain.
Mr Litvinenko, who had been a vocal critic of the Kremlin, issued a statement on his deathbed accusing Russian President Vladimir Putin of ordering his poisoning, but this has been dismissed by the Kremlin.
The 43-year-old died in a London hospital on 23 November after apparently being poisoned by polonium-210.
He had fallen ill on 1 November after a series of meetings in London.
One of them, at the city's Millennium Hotel, involved Mr Litvinenko, former KGB officer Andrei Lugovoi, Mr Lugovoi's business associate Mr Kovtun and a fourth man, Vyacheslav Sokolenko.
Their meeting has become the main focus of the police inquiry.
Mr Lugovoi was this week due to have met British officers investigating Mr Litvinenko's death, but that did not happen.
He and Mr Kovtun are both currently undergoing medical checks in Russia, but there have been conflicting reports about their health.
Mr Lugovoi's lawyer said his client's condition should not have prevented him from being questioned.
Mr Kovtun has been reported as being in a coma and also suffering from radiation damage to his intestines and kidneys, but this has been denied by Mr Lugovoi's lawyer, Andrei Romashov.
Meanwhile, it has emerged that seven bar staff who were working at the Millennium Hotel's Pine Bar on 1 November have tested positive for low levels of polonium-210.
The Health Protection Agency (HPA) said they faced "no health risk in the short term", but the concern was that they may be at a very small increased risk of cancer in the long term.
It stressed the risk to the general public was likely to be "very low".
The HPA has asked anyone who was at the Pine Bar between 31 October and 2 November to contact NHS Direct.