Yulia and Sergei Skripal, 66, were found slumped unconscious on a public bench in the English city of Salisbury on March 4. Britain said they were poisoned with a military-grade nerve agent, the first known use of such a toxin on European soil since World War Two.
London has blamed Russia for the attempted murder while Moscow denies any involvement. The incident has had major diplomatic ramifications, with mass expulsions of Russian and Western diplomats.
The attack left the Skripals in a critical condition and doctors had initially feared that even if they did survive, they might have suffered permanent brain damage.
But while her father remains stable in intensive care, Yulia's health has improved rapidly. On Thursday she issued a statement through British police to thank hospital staff and people who came to her help when "when my father and I were incapacitated".
Her recovery means she can help British counter-terrorism police with their investigation although she did not give any details about what had happened in her brief remarks.
Britain's Foreign Office said she had been offered assistance by Russia's embassy but had so far declined.
"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," said Yulia, 33.
"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."
Hours before the statement issued by British police, Russian state TV and Interfax reported that Yulia 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.
Asked about her father's health, Yulia was cited as saying: "Everything is fine, he is resting right now, sleeping ... nobody has any problems that can't be put right."
Russian state TV said it could not vouch for the authenticity of the quotes. Viktoria Skripal has said she plans to travel to England if she can get a visa.
Police believe the nerve agent was left on the front door of the home in Salisbury where Skripal, a military intelligence colonel who betrayed dozens of Russian agents to Britain's MI6 spy service, lived after he was freed in a spy swap.
The attack has driven Moscow's relations with the West to a new post-Cold War low, with Britain and its allies, including the United States, expelling about 130 diplomats and the Kremlin responding in kind.
The United Nations Security Council will meet later on Thursday to discuss the British accusations at Moscow's request.
Russian Deputy U.N. Ambassador Dmitry Polyanskiy said on Twitter it was "highly likely there will be a moment of truth" during the meeting.
"Those who spread lies about alleged Russian involvement in #SalisburyPoisoning must understand that such irresponsible behaviour has its price," he added. "We on the contrary have nothing to hide."
British U.N. Ambassador Karen Pierce responded: "There's a part of me that's tempted to say 'bring it on'. We are confident of our position, we have set it out very clearly."
On Wednesday, Russia lost its call for a joint inquiry to be held into the poisoning at a meeting of global watchdog the Organisation for the Prohibition of Chemical Weapons.
Moscow's ambassador to London Alexander Yakovenko said on Thursday Russia had never made Novichok, the Soviet-era nerve agent which British experts say was the toxin used.
He said the Kremlin would accept the results of OPCW tests but only if there was transparency and they were confirmed by experts from outside Europe and NATO.
While scientists at the Porton Down biological and chemical weapons laboratory near Salisbury have concluded the toxin was Novichok, its chief executive said on Tuesday they had not yet determined whether it was made in Russia.
That prompted even some allies to say London needs to provide more evidence of Russian culpability.
Britain says there is no plausible explanation other than that Russia was behind the attack and Foreign Secretary Boris Johnson has accused Russia of running a disinformation campaign.
A number of Russians have died in mysterious circumstances in Britain in recent years including dissident Alexander Litvinenko who was poisoned with a rare radioactive isotope in 2006. A British inquiry concluded his murder had probably been ordered by Russian President Vladimir Putin.
"We have a lot of suspicions about Britain," said Russian UK ambassador Yakovenko. "If you take the last 10 years, so many Russian citizens died here in the UK, under very strange circumstances ... My question is why is it happening here?"