Speaking to Reuters at an undisclosed location, she describes her shock at what happened to her and her father Sergei and asks for their privacy to be respected.
Yulia said she was grateful for offers of help from the Russian Embassy but "at the moment I do not wish to avail myself of their services". Later, London stated that this agent was designed in Russian Federation and blamed Moscow for being behind the incident based on this assumption.
Britain says the Russian state poisoned the Skripals with a Soviet-designed nerve agent dubbed Novichok that likely was smeared on the door handle of Sergei Skripal's suburban house.
"I still find it hard to come to terms with the fact that both of us were attacked".
Yulia Skripal said that "in the longer term I hope to return home to my country".
Viktoria also said she was happy that Yulia was "safe and sound".More news: Opioids found in Puget Sound mussels
Even so, a United Kingdom chemical weapons lab known as Porton Down, which had been tasked with examining the poison that was used on the Skripals, said it could not say for sure who manufactured it other than that it was "probably only within the capabilities of a state actor".
During their "slow and extremely painful" recovery, she has been struggling to come to terms with "the devastating changes thrust upon me both physically and emotionally", she said.
She was discharged from Salisbury District Hospital about five weeks after the poisoning and has not been seen by the media until now.
The March attack on the Skripals led to comparisons with the death of Alexander Litvinenko, a former Russian intelligence officer who defected to Britain and died in 2006 after being exposed to polonium-210, a rare radioactive isotope.
The UK responded to the attack, which it blames Russia for, by announcing a number of sanctions including the expulsion of 23 Russian diplomats.
Ms Skripal, who was attacked on 4 March and left hospital on 9 April, said in a pre-prepared statement filmed by the Reuters news agency at an unspecified location in London: "I still find it hard to come to terms with the fact that both of us were attacked". She reiterated her words in a handwritten statement.More news: Tesla agrees to settle class action over Autopilot billed as 'safer'
Detectives have said that novichok was smeared on the front doorhandle of Sergei Skripal's semi-detached Salisbury home.
Yulia Skripal's statements need to be checked to make sure that they were made voluntarily, said Kremlin Spokesman Dmitry Peskov in an interview with TV channel NTV. "Also, I want to reiterate what I said in my earlier statement, that no one speaks for me, or for my father but ourselves", she said. Russian President Vladimir Putin recently noted that if Novichok had been used, the Skripals would have died nearly instantly.
"Overall, considering we are talking about a fairly unprecedented worldwide provocation against Russian Federation that was unleashed by Britain and London, we maintain our distrust and have every reason to do so".
Skripal arrived in Britain from Russian Federation at London's Heathrow Airport on March 3 on one of her regular visits to see her father.
Moscow accuses Britain of failing to provide any evidence for its claims and of stonewalling Russian requests for information.
"I am grateful to all of the wonderful, kind staff at Salisbury hospital, a place I have become all too familiar with".More news: Klopp says Salah 'full of power' regardless of Ramadan plans