Lavrov said that Russia and Britain believed Litvinenko's death should not be politicised.
He said: "If there are any questions, they should be put through law enforcement agencies."
John Reid, the British home secretary, said in Brussels that Moscow had "assured us we'll get all the cooperation necessary".
Associates of Litvinenko have alleged either Kremlin involvement in his killing or that rogue elements in Russia's state security service were responsible.
Before he died Litvinenko, a former Russian state security service agent who became one of Vladimir Putin's sharpest critics in the London-based Russian emigre community, accused Putin of ordering his death.
|Lavrov said that Russia and Britain believed Litvinenko's death should not be politicised.|
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The Kremlin has denied any part in the killing, and Kremlin opponents also find the theory of Putin's involvement highly improbable, noting that such a high-profile killing on foreign soil could only damage him.
Italy's foreign minister said he would ask Putin in Moscow on Tuesday to help the British police in their investigation.
The British detectives are likely to try to interview Russian citizens who met Litvinenko at London's Millennium Hotel on November 1, the day he fell ill.
Andrei Lugovoy, a former KGB agent, says he and Dmitry Kovtun, a businessman, met Litvinenko that day at the hotel. But Lugovoy, now back in Moscow, says they discussed a business opportunity and denies anything to do with an attempt on Litvinenko's life.
Alex Goldfarb, a London-based friend of Litvinenko, said the British investigators should see another ex-KGB agent, Mikhail Trepashkin, who had what he called "substantive information".
Trepashkin, serving a four-year sentence in an Urals prison for divulging state secrets, said in a letter last Friday that the FSB, the Russian state security service, had created a hit squad to kill Litvinenko and other enemies of the Kremlin.
Britain's Health Protection Agency said on Monday that two more hotels in central London had been checked for radiation as part of the investigation. Several other locations in the capital and some aircraft have also been checked amid a public health scare.
One was the Parkes Hotel in Knightsbridge. The Sunday Times newspaper said this was where Lugovoy stayed when he visited London on his first of three trips in October.
The agency has so far tested 99 urine samples.
It said: "The only urine sample that the agency has examined that has shown higher levels of polonium 210, relates to an adult family member [of Litvinenko]."
Earlier officials said that a female relative of Litvinenko - reported to be his widow Marina - had traces of polonium 210 in her urine. They said she was not in short-term danger and any long-term risk was likely to be small.
Gaidar sent home
Yegor Gaidar, architect of Russia's market reforms, was released from a Moscow hospital late on Monday where he was taken after collapsing at a conference in Ireland, his spokesman said.
Earlier in the day, Russian doctors, at a loss to explain Gaidar's ailment, held a consultation in order to diagnose him.
Gaidar, 50, will continue treatment at home.
Gaidar, a former acting prime minister and now an influential academic, was taken to hospital last month shortly after Litvinenko's death.
Irish officials say no radiation has been found at sites in Ireland visited by Gaidar.
The Kremlin said last week that Putin had telephoned Gaidar to wish him a speedy recovery.