Mr Lavrov said the British government had refused to provide Moscow access to materials and samples related to the case.
He called it a violation of the Chemical Weapons Convention, which outlaws the production of chemical weapons.
Moscow was willing to cooperate with the probe but suggested the UK would be “better off” complying with its international obligations “before putting forward ultimatums," Mr Lavrov added.
On Monday, Theresa May said Mr Skripal and his daughter, Yulia, had been poisoned with a military-grade nerve agent known as Novichok, which had been developed in the Soviet Union.
She said Russia has until the end of Tuesday to explain how the substance ended up in Britain, otherwise, she said, the attack will be interpreted as an act of military aggression.
The British government will have understood that the Kremlin was unlikely to respond to Ms May’s ultimatum positively. Many in Moscow are already bracing themselves for that they see as an inevitable tightening of sanctions.
Sergei Stepashin, Vladimir Putin’s predecessor as FSB director and Prime Minister, also called for British authorities to hand over evidence.
“We have the relevant agreements to investigate this together,” he told the Interfax news agency.
Mr Stepashin said British security services may have been complicit in the poisoning — and were using it to undermine Russia ahead of Sunday’s presidential elections: “It seems obvious to me that this might be the primitive work of English security services. Tell me who needs this traitor in Russia?”
There could be another reason apart from elections, he added: “The World Cup is about to take start and the English hate us for the fact the competition is taking place in our country.”
Earlier in the day, Konstantin Kosachyov, head of the Committee for Foreign Affairs in the Russian upper house described British allegations as “maniacal.” Britain was well versed in blaming all kinds of “mortal sins” on Russia, he wrote on Facebook.
“Russia is being asked to justify itself even without evidence,” he said. “In queen of courts of Britain, this degradation is complete: the total presumption of guilt, when the neither court and nor prosecutor are asked to prove the case, but the accused ”
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