In her first televised statement, Yulia Skripal said she wants to return to her country "in the longer term", despite being poisoned with a nerve agent.
Ms Skripal and her father Sergei, a former double agent, were found poisoned on 4 March in the centre of Salisbury, and were only discharged from hospital after weeks of treatment during which it was feared they would die.
Chemical investigators established that the pair were poisoned with a form of chemical agent known as Novichok, produced in the former Soviet Union. The UK Government has said it believes the Russian government is culpable for the attack.
Both the Skripals are being housed in an undisclosed location for their protection. Speaking into a camera with a tracheotomy scar visible on her neck, Ms Skripal said: "I came to the UK on the 3rd of March to visit my father, something I have done regularly in the past.
"I still find it difficult to come to terms with the fact that both of us were attacked. We are so lucky to have both survived this attempted assassination. Our recovery has been slow and extremely painful.
"The fact that a nerve agent was used to do this is shocking. I don't want to describe the details but the clinical treatment was invasive, painful and depressing."
Paying tribute to those who aided her recover, she added: "I am grateful to all of the wonderful, kind staff at Salisbury hospital, a place I have become all too familiar with. I also think fondly of those who helped us on the street on the day of the attack.
"I was discharged from hospital on the 9th of April and continue to progress with treatment but my life has been turned upside down as I try to come to terms with the devastating changes thrust upon me both physically and emotionally.
"I take one day at a time and want to help care for my Dad till his full recovery. In the longer term I hope to return home to my country."
Russian diplomats and government officials have demanded consular access to the Skripals, which Yulia has previously refused, and Russian sources have suggested the pair are being held by UK authorities against their will.
Russian media and social media accounts have circulated conspiracy theories that the Skripals were prisoners, had been poisoned by British agents, and were in fact dead.
Ms Skripal continued: "I wish to address a couple of issues directly and have chosen to interrupt my rehabilitation to make this short statement. I ask that everyone respects the privacy of me and my father. We need time to recover and come to terms with everything that has happened.
"I'm grateful for the offers of assistance from the Russian Embassy but at the moment I do not wish to avail myself of their services.
"Also, I want to reiterate what I said in my earlier statement that no one speaks for me, or for my father, but ourselves."