A friend of a former Russian spy seriously ill in a London hospital said both had received e-mail threats days before his poisoning.
Italian Mario Scaramella told a Rome press conference that he met Alexander Litvinenko the day he fell ill.
Scotland Yard anti-terrorist officers have taken charge of the investigation.
Meanwhile, doubts persist over whether the substance responsible for Mr Litvinenko's illness was the toxic metal thallium, or some other poison.
Toxicologist Professor John Henry said at University College Hospital that the poison may have been a radioactive form of thallium, which would now be difficult to trace, but that some other substance was also involved.
Meanwhile, officers are treating the case as a suspected "deliberate poisoning" and say it could have taken place in the last two weeks.
Police have not yet identified the 'time window' in which the poisoning was administered.
The doctor treating the former spy said in the hospital's first official statement that the cause may never be found.
Dr Amit Nathwani said it was possible he may not have been poisoned by thallium, adding that he could not be sure because of the time he presented himself to University College Hospital.
The consultant said his patient was seriously ill but stable - a situation which had not deteriorated substantially in the last day.
He added that moving him into intensive care had been a precautionary measure.
Dr Nathwani also complained that media interest in the case had become "somewhat intrusive".
BBC Rome correspondent Christian Fraser said Mr Scaramella, who is involved in an Italian parliamentary inquiry into KGB activity, was sufficiently worried by the contents of an e-mail to ask for advice from Mr Litvinenko.
He said he met the Russian in a London sushi bar on 1 November for 35 minutes to discuss the e-mail.
He said Mr Litvinenko had promised to look into the message but when Mr Scaramella called him later that night the Russian was already falling ill.
Meanwhile, detectives are planning to travel to Italy to interview Mr Scaramella and are also investigating whether Mr Litvinenko was being followed.
Dr Henry said Mr Litvinenko, 43, had symptoms consistent with thallium poisoning but other symptoms linked to other substances.
Mr Litvinenko fled to the UK in 2000 and was granted asylum
He said Mr Litvinenko's bone marrow was not functioning and his white cell count has dropped to zero.
"Something other than thallium is involved," he said.
Radioactive thallium is used in hospitals, but Dr Henry said it was not used in massive doses consistent with Mr Litvinenko's condition.
"Poisons can be taken by mouth, they can be injected, they can be inhaled," he said.
"In this case his symptoms are gastro-intestinal so the probability is that he has swallowed something that is poisoned.
Friends of Mr Litvinenko have alleged he was poisoned because he was critical of the Russian government.
Kremlin spokesman Dmitry Peskov said they did not want to comment about the accusations, which they called "sheer nonsense".
Russia's foreign intelligence service also denied involvement.
Mr Litvinenko had been investigating the murder of Russian journalist Anna Politkovskaya, an outspoken critic of Mr Putin and Russian policy in Chechnya, who was shot dead at her Moscow apartment building last month.