Yulia Skripal has made her first public comment since being poisoned in Britain last month along with her ex-Russian agent father Sergei, saying the "entire episode is somewhat disorientating".
The Skripals were found slumped on a bench in the southern English city of Salisbury on March 4 in a nerve agent attack that the British government has blamed on Russia, with what it says was a military-grade Novichok nerve agent.
"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," Yulia Skripal, 33, said in a statement issued by London police on Thursday.
"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."
Russia's ambassador to Britain Alexander Yakovenko said he was happy to hear that Ms Skripal was recovering.
Russia denies any involvement but the crisis has led to the worst diplomatic crisis between Russia and Western nations since the Cold War.
Mr Yakovenko was part-way through a news conference at his official residence in London when Ms Skripal's statement was issued.
Asked about the statement by a reporter, Mr 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."
Ms Skripal said she wanted to thank the hospital staff treating her and the people who came to her help when "when my father and I were incapacitated".
The attack left the Skripals in critical condition but on March 29, the hospital where they are being treated said Ms Skripal was getting better.
Hospital bosses said her father was still in a critical but stable condition in an intensive care unit.
Earlier on Thursday, Russian state TV and Interfax reported that Ms Skripal had phoned her cousin Viktoria Skripal in Russia, saying she and her father were both recovering and that she expected to leave hospital soon.
"Everything is fine, everything is fixable, everyone is getting better, everyone is alive," they quoted her as saying in the call.
When asked about her father's health, Ms Skripal was cited by them as saying: "Everything is fine, he is resting right now, sleeping. Everyone's health is fine, nobody has any problems that can't be put right. I will soon be discharging myself."
Russian state TV said it could not vouch for the authenticity of the quotes.
Viktoria Skripal, Sergei's niece, has said she plans to travel to England and try to bring her cousin back to Russia.