Speculation is mounting that Sergei Skripal and his daughter Yulia could be able to offer officers investigating the Salisbury nerve agent attack missing clues as the pair continue to recover.
The former double agent is "responding well to treatment, improving rapidly and no longer in a critical condition", Salisbury District Hospital said.
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 March 4.
Foreign Secretary Boris Johnson said the improvement in the condition of Mr Skripals was "great news" and "testament to the quick work" of the emergency services.
Police believe Mr Skripal and his daughter, who was visiting him from Russia, first came into contact with the Novichok agent at his home in Salisbury, Wiltshire.
Ms Skripal made her first public comments on Wednesday shortly after Russian TV reported that she had contacted her cousin Viktoria in Moscow to say she and her father were recovering and that she would soon be discharged.
The UK authorities have refused to grant Viktoria Skripal a visa to come to Britain, with the Home Office saying her application "did not comply with the immigration rules".
The improvement in Mr Skripal's condition was revealed by Dr Christine Blanshard, medical director at Salisbury District Hospital, who said speculation about when the two could be released from hospital was "just that - speculation".
The Foreign Office said the pair were "likely to have ongoing medical needs".
The Russian Embassy said it hoped the improvement in the Skripals' health will "contribute to the investigation of the crime perpetrated against them".
Moscow has denied being responsible for the poisoning of the Skripals but the incident has plunged diplomatic relations between Russia and the West into the deep freeze.
A Foreign Office spokesman said: "We are very pleased that both Mr Skripal and his daughter Yulia are improving. This is a tribute to the hardworking and talented NHS staff in Salisbury who have provided outstanding care.
"The NHS will continue to provide ongoing care for the Skripals, both of whom are likely to have ongoing medical needs.
"Let us be clear, this was attempted murder using an illegal chemical weapon that we know Russia possesses."
Meanwhile, Russia continued to raise questions about the fate of the pets at Mr Skripal's home.
Two guinea pigs were found dead at the property and a cat, which was found in a distressed state at the house, was put down.
The Russian Embassy said: "Regarding the dead guinea pigs and the malnourished cat, it is said unofficially that they were taken to the Porton Down facility and incinerated there.
"But it remains unclear if their remains were ever tested for toxic substances, which would constitute useful evidence, and if not, why such a decision was made.
"Overall, it is difficult to avoid the impression that the animals have been disposed of as an inconvenient piece of evidence."