The investigators are in Moscow to question several Russians who met with Litvinenko in London, where he died after being poisoned with a radioactive isotope, polonium-210.
It remains unclear if Litvinenko was intentionally poisoned. Scotland Yard, the headquarters of the London metropolitan police service, is not expected to comment while the investigation is under way.
The date of his funeral is due to be set later this week.
Litvinenko's father, Valter, told RFE/RL's Russian Service his son converted to Islam shortly before his death and wished to be buried according to Muslim tradition.
"He told me about his decision two days before he died. He said, 'Papa, I have to talk to you about something serious. I've become a Muslim,'" Walter Litvinenko said.
"I said, 'Sasha, it's your decision. As long as you don't become a communist or a satanist, that's the main thing.' I'm a Christian myself, but I have a granddaughter whose father is Kabardin -- my daughter's husband, he's Muslim as well," he continued. "We haven't lost God; we believe in God. But how to believe in God, how to pray -- everyone should do that in the way they consider best."
Valter Litvinenko, who described the conversion as "an important personal decision," said his son had been thinking about becoming a Muslim for some time because of growing disenchantment with the Russian Orthodox Church.
Akhmed Zakayev, the London-exiled Chechen separatist envoy, told RFE/RL that Litvinenko asked him about the possibility of converting in the early days of his illness.
"I told him it was a purely personal matter, that it isn't important to which god we pray as long as we aren't doing ignoble acts," Zakayev said. "And I sort of dropped it. But he over and over again returned to the subject."
Zakayev added that Litvinenko went on to pronounce the shahadah, the fundamental Muslim statement of faith.
"Any student of Islam will tell you that there are no particular rituals for converting to Islam. All you have to do is say one sura" -- a verse or chapter from the Koran -- "and from that moment if the person who pronounces this sura, this shahadah, has sincere intentions, from that moment he is considered a Muslim," he said.
Zakayev said despite the harshly debilitating effects of Litvinenko's illness, he remained of sound mind. Just days before his death, Zakayev said, Litvinenko worked for 16 hours with police officers investigating his poisoning.
Zakayev said Litvinenko remained hopeful he would recover. One day before his death, however, Litvinenko asked Zakayev to bring an imam to his hospital room to perform last rites.
"On November 22, at his request, I, with his wife's approval, brought an imam to him," Zakayev said. "He read over him a sura from the Koran, the one that is read over a dying Muslim."
Zakayev noted that, according to Muslim ritual, prayers are conducted over the body before burial. Now, he added regretfully, " that part of the process which Aleksandr requested cannot be fulfilled because of the exceptional circumstances of the radiation in his body and the fact that the coffin that will contain his body cannot be opened for 6 1/2 years."
British investigators in Moscow plan to interview three men who may have information about Litvinenko and how he came to be poisoned with polonium-210.
The men -- Andrei Lugovoi, Dmitry Kovtun, and Vyacheslav Sokolenko -- met with Litvinenko in a London hotel on November 1, the day he fell ill. All three have protested their innocence, and say they are being framed.
Prosecutor-General Yury Chaika speaking to journalists in Moscow today (epa)
It was not clear if the investigators would gain access to Lugovoi. The former Russian intelligence officer underwent radiation tests last week and has reportedly checked into hospital for further tests.
Prosecutor-General Yury Chaika said today that Russian prosecutors will question Lugovoi. He also said that any Russian citizen implicated in the case would be tried in Russia, not Britain.
Meanwhile, a spokesman for Russia's prison service is quoted by Interfax as saying the British team will not be granted access to former intelligence agent Mikhail Trepashkin, who is now in prison. Trepashkin's lawyers said earlier Trepashkin had information relevant to the Litvinenko investigation. Widening Investigation
A separate contingent of Scotland Yard investigators was in the United States last week to question a former KGB agent with ties to both Litvinenko and Litvinenko's London ally, exiled Russian billionaire Boris Berezovsky.
The man, Yury Shvets, told The Associated Press he had given the British officers the name of the person he believes is behind Litvinenko's death. He declined to elaborate.
The widening investigation follows revelations last week that radioactive traces had been found on airplanes that traveled between London and Moscow, as well as to a dozen other European cities during the month of November.
A fourth man who met Litvinenko on the day of his apparent poisoning has also been found to have come in contact with polonium-210.
Mario Scaramella, an Italian security consultant, is currently in London's University College Hospital. Doctors say he remains well and has no external symptoms of poisoning with polonium-210.
In the November 1 meeting, held at a London sushi restaurant, Scaramella reportedly gave Litvinenko a memo that claimed Russian security service officers and a little-known organization called Honor and Dignity were trying to kill both Litvinenko and Berezovsky.
Britain's "Daily Telegraph" newspaper reported that the memo contained a hit list that also included Scaramella and journalist Anna Politkovskaya, who was shot dead in an apparent contract killing in October. 'First-Class' Killing
The revelations have focused attention on Honor and Dignity, which is led by Valentin Velichko, a veteran of the Federal Security Service (FSB). Velichko has so far declined comment on the case.
Oleg Gordiyevsky, a former officer with the FSB's predecessor agency, the KGB, told RFE/RL he did not believe Honor and Dignity was responsible for Litvinenko's poisoning.
"Such an organization would not be able to carry such a high-grade killing as Litvinenko's in London," Gordiyevsky said. "Litvinenko's killing is a first-class, highly professional KGB operation -- the SVR [Russia's foreign intelligence agency] and the FSB combined. No amateur organization would ever be able to obtain this highly toxic material."
The operation, Gordiyevsky said, was carried out according to what he called the "best" KGB rules.
The only flaw, he added, was that the perpetrators failed to consider that the British had the high-grade equipment needed to follow the radioactivity trail to Moscow. The plotters, he said, thought such technology was available only to Russians.
Litvinenko and his supporters were firm in their belief that Russia's security services and the Kremlin -- and more specifically, Russian President Vladimir Putin -- were behind his poisoning.
Russia has angrily denied any involvement in the case. Putin, himself a prominent KGB graduate, said Litvinenko's death was the work of forces in the West looking to discredit Russia.
Gordiyevsky, however, says he has little doubt that it is Russia's security services -- and by extension, the ruling elite -- that are behind the murder plot.
"Special services are the ruling party in Russia," he said. "They have replaced the Communist Party of the Soviet Union, so they do whatever they want. Their influence is everywhere."
"First of all, the president is from special services," he added. "The vice [prime minister] is from special services, the prime minister is from special services" -- Mikhail Fradkov in fact served with the Federal Tax Police -- "and most Duma members are FSB agents."