The former Russian double agent poisoned with a nerve agent is no longer critically ill in hospital.
Doctors said Sergei Skripal was “responding well to treatment, improving rapidly and no longer in a critical condition”.
Mr Skripal, 66, and his 33-year-old daughter Yulia were left fighting for their lives in hospital after being found unconscious on a park bench in Salisbury on 4 March.
Police have claimed Mr Skripal and his daughter, who was visiting him from Russia, first came into contact with the Novichok agent at his home in Wiltshire.
Ms Skripal made her first public comments on Wednesday shortly after Russian TV reported she had contacted a relative in Moscow to say she and her father were recovering and she would soon be discharged.
Dr Christine Blanshard, medical director at Salisbury District Hospital, said: “Last Thursday, I informed you that Yulia Skripal’s condition had improved to stable. As Yulia herself says, her strength is growing daily and she can look forward to the day when she is well enough to leave the hospital.
READ MORE: Salisbury poisoning: Porton Down can’t verify nerve agent is Russian
“Any speculation on when that date will be is just that – speculation. In the meantime, Yulia has asked for privacy while she continues to get better – something I’d like to urge the media to respect.
“I also want to update you on the condition of her father, Sergei Skripal. He is responding well to treatment, improving rapidly and is no longer in a critical condition.”
Reacting to reports of Mr Skripal’s improved condition, the Russian Embassy to the UK tweeted: “Good news!”
Russia has appealed for the UK to issue visas for relatives to visit the Skripals in hospital in Salisbury where they are being treated for exposure to the deadly chemical.
The Kremlin has warned Britain is “playing with fire and will be sorry” over the poisonings as the two countries traded jibes at the United Nations.
Russian UN ambassador Vasily Nebenzya claimed the UK’s main argument about the “unquestionable Russian origin” of the Novichok agent was “no longer valid” following comments from Porton Down’s Gary Aitkenhead.
Moscow called the UN Security Council meeting to discuss the incident, with foreign minister Sergey Lavrov saying the UK had “legitimate questions” to answer about what happened. But security minister Ben Wallace said it was “beyond reasonable doubt” Russia was to blame for the attack as the UK sought to maintain diplomatic pressure over the incident.
Russia has lost a vote in The Hague on its demand for its experts to be involved in testing samples of the substance used in the Salisbury attack.