Today's development could prove key to the investigation into the attack, as Yulia could soon be able to tell police about the moments before they collapsed in a park.
The Foreign Office said it has conveyed to Yulia the Russian embassy's offer of consular assistance and that she "she is now able to choose if and when to take up this offer but to date she has not done so".
In her first statement since coming out of a coma, Yulia said: "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."
She thanked healthcare workers at Salisbury District Hospital as well as "the people of Salisbury that came to my aid when my father and I were incapacitated".
She added: "I am sure you appreciate that the entire episode is somewhat disorientating.
"I hope that you'll respect my privacy and that of my family during the period of my convalescence."
It comes after Skripal's niece Viktoria revealed that she had received a phone call from Yulia at 10.30am this morning.
Viktoria, who is trying to secure a visa in order to visit her relatives, said: "It is a feeling of enormous relief to hear from her."
The recording has not been independently verified but Viktoria said she was convinced she was talking to Yulia.
Yulia's statement was issued through the Metropolitan Police while the Russian Ambassador addressed the media at the Russian Embassy in London.
He said he would "meet personally" with Viktoria Skripal 'when she comes to London'.
When told that Yulia Skripal had issued a statement, Yakovenko said he wanted to "congratulate my compatriots that they are well".
The ambassador was pressed on the embassy's jokey tweets about the attack and insisted Russia was not treating the incident as a game.
"We are taking this seriously," he said.
Responding to the claim that Russia had a motive to target Skripal, he said: "It's not true. Absolutely not true.
"We hear all the stories and the theories about our motivations. We don't buy it. For us, these kinds of statements are unacceptable."
Last week, the Russian Embassy seized upon reports that Yulia was conscious to demand that its remaining diplomats in London are allowed to see her.
Britain is currently fighting an information war with the Kremlin after Theresa May accused Russia of being behind the nerve agent attack.
Britain may now be forced to let agents of the Russian state visit the citizen the country is accused of attempting to murder.
She could also potentially identify whoever carried out the attack - which is now thought to have taken place at the Skripals' suburban home.
The Metropolitan Police believe Skripal and his daughter, who was visiting him from Russia, first came into contact with the deadly chemical at his home in Salisbury.
