The Skripals were poisoned by what London claims is an A234 nerve agent in England on March 4.
"As far as we know from the literature, there is no specific antidote for Novichok", Ralf Trapp, an expert on chemical weapons, told AFP, referring to a batch of nerve agents allegedly developed by Moscow in the Soviet era.
Following the update on Mr Skripal's condition, the Russian Embassy tweeted: "Good news!"
The next day, Medical Director at Salisbury District Hospital, stated that Sergei Skripal was responding well to treatment and was improving quickly.
"Mr. Skripal and his daughter were poisoned with a military-grade nerve agent of a type developed by Russian Federation", specifically from the Novichok group, British Prime Minister Theresa May said following the attack.
Russian Federation has said it does not have such nerve agents and President Vladimir Putin dismissed as nonsense the notion that Moscow would have poisoned Skripal and his 33-year-old daughter.
Russian President Vladimir Putin has denied Moscow's involvement in the attack, suggesting that Britain had carried it out to stoke anti-Russian hysteria.
The US unveiled new sanctions Friday against seven of Russia's most influential oligarchs, to which Moscow promised a "tough response".
The first public comments by Yulia Skripal since the poisoning emerged on Thursday.
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A British Foreign Office spokesperson praised medical staff continuing to treat the pair but said they were "likely to have ongoing medical needs". Sergei is recovering well and out of danger but the pets have not been the lucky ones. "We don't know if that's because she had less administered, or it took longer to have an effect or because she's younger or healthier - there's too many factors to take into account", she said.
Yulia's health has also improved rapidly.
The ambassador held a 90-minute press conference this week in which he denied Russian Federation had ever produced novichok and suggested Britain may be behind the poisoning.
It's believed their recovery could help British counter-terrorism police solve how they were attacked. "We have therefore officially requested the Foreign Office to provide us with the respective information, including on whether the animals are receiving any treatment". Victoria Skripal told Sky News that the "British must have something to hide" after the decision.
In a separate announcement, the United States imposed major sanctions on Friday against 24 Russians in one of Washington's most aggressive moves to punish Moscow for what it called a range of "malign activity", including alleged meddling in the 2016 USA election.
A request from Russian Federation to be part of a joint investigation into the poisoning was denied by the Organisation for the Prohibition of Chemical Weapons, with the United Kingdom likening the proposal to an arsonist investigating his own fire.
Sergei Skripal was a double agent who sold secrets to Britain. Forensic analysis revealed that Skripal and his daughter first came into contact with a nerve agent at their house, with the highest concentration of it found on their front door.
Whether the Skripal family had a second cat is not immediately clear. His guinea pigs were discovered dead.