It comes hours after Russia aired a phone conversation by a woman claiming to be Ms Skripal
Russian spy poisoning: Yulia Skripal says her strength is 'growing daily'
Yulia Skripal, who was poisoned along with her father Sergei Skripal in Britain last month, has released a statement through UK police after Russian state TV aired an alleged phone conversation between Ms Skripal and a relative.
Last week, officials from Salisbury NHS Trust, which oversees the hospital where the Skripals are being treated, said the 33-year-old's condition was improving rapidly and she was no longer in a critical condition.
“I woke up over a week ago now and am glad to say my strength is growing daily. I am grateful for the interest in me and for the many messages of goodwill that I have received," the statement issued on behalf of Ms Skripal reads.
“I have many people to thank for my recovery and would especially like to mention the people of Salisbury that came to my aid when my father and I were incapacitated. Further than that, I would like to thank the staff at Salisbury District Hospital for their care and professionalism.
“I am sure you appreciate that the entire episode is somewhat disorientating, and I hope that you’ll respect my privacy and that of my family during the period of my convalescence.”
Just hours earlier Russian state television aired what it said was a phone conversation between Ms Skripal and her cousin Viktoria.
The woman in the call introduces herself as Yulia Skripal in Russia and says that she expects to be discharged from hospital soon.
"Everything is fine [with my father]. He is resting now, he is sleeping. Everyone's health is fine. There is nothing that is irreversible. That's it, I'll be discharged soon. Everything is OK," she says.
Rossiya 1 television's "60 Minutes" talk show said the recording had come from Ms Skripal's cousin Viktoria but that they could not confirm the authenticity.
In the phonecall, the woman who answers to the name Viktoria says she plans on visiting the UK
The presumed cousin, who lives in Russia, responds saying she was hoping to come to the UK next week.
But the alleged Yulia replies: "Vika, nobody will give you a visa."
Ms Skripal's father, a former Russian double agent, remains in critical condition but is stable, according to the latest update.
Russia's ambassador to the UK, who was giving a press conference in London when the statement was released, said he believed Ms Skripal would return to Moscow, where she had been living and working before the attack.
When asked about Ms Skripal's improved health, Alexander Yakovenko said: "I am really happy and I hope that Sergei Skripal will also recover. I am quite sure that one day Yulia will come back to Moscow."
The ambassador denied Russian involvement in the nerve agent attack on March 4, adding that Moscow had no motive to carry out the crime.
Britain has said it is "highly likely" that Russia was behind the attack, which has caused increased tensions between the Kremlin and the West.
On Tuesday, scientists at Porton Down, Britain's defence laboratory, identified the nerve agent Novichok as the substance used in the attack but said they could not confirm its source.
Russian demands to be involved in the investigation into the Skripal attack were rejected during a meeting at The Hague-based Organisation for the Prohibition of Chemical Weapons (OPCW) on Wednesday.
The proposal was dismissed by 15 votes to six with 17 member states abstaining.
Russian Foreign Minister Sergei Lavrov said the number of abstentions from the vote showed that there were doubts about the UK's claims.
"It's unacceptable to make unfounded accusations instead of conducting a fair investigation and providing concrete facts," Mr Lavrov said on Thursday. "Yesterday's debate in The Hague showed that self-respecting adults don't believe in fairy tales."