Yulia Skripal has said she wants to go back to Russia "in the longer term", after she and her father were poisoned with a nerve agent.
Ms Skripal, 33, and former Russian spy Sergei Skripal, 66, were exposed to the novichok agent on March 4 in Salisbury.
They were both admitted to Salisbury District Hospital along with Detective Sergeant Nick Bailey.
Mr Skripal left the hospital on Friday, following his daughter's discharge on April 9.
"I still find it difficult to come to terms with the fact that both of us were attacked," Ms Skripal continued.
"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."
Ms Skripal described her treatment as "invasive, painful and depressing" and said she is "grateful to all of the wonderful, kind staff at Salisbury hospital".
"I also think fondly of those who helped us on the street on the day of the attack," she added.
Ms Skripal gave a statement to press on Wednesday at a location in London and asked for privacy for herself and her father.
"We need time to recover and come to terms with everything that has happened," she added.
"I was discharged from hospital on April 9 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.
"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."
The Russian Embassy responded with a statement saying it is "glad to have seen Yulia Skripal alive and well" and repeated its request to see the Skripals.
"The UK is obliged to give us the opportunity to speak to Yulia directly in order to make sure that she is not held against her own will and is not speaking under pressure," it continued.
"So far, we have every reason to suspect the opposite."
The British Government said it is "highly likely" the Kremlin was behind the attack, which the Russian government has repeatedly denied.
Moscow's ambassador to the UK Alexander Yakovenko has demanded the right to see the Skripals, claiming the UK was flouting international law by refusing consular access.