The Russian Embassy in London has previously said it had not been granted consular access to the 33-year-old woman.
Yulia Skripal said she was treated "with obvious clinical expertise and with such kindness".
Skripal said she was not yet strong enough to give a media interview and she said comments made by her cousin to Russian media were not her's nor those of her father.
"I thank my cousin Viktoria for her concern for us, but ask that she does not visit me or try to contact me for the time being," the statement quoted her as saying.
Viktoria last week said she had been denied a visa to visit her family in the UK and expressed concern over their lack of contact. She also appeared to cast doubt over the British Government's version of events.
-DPA , Reuters, AAP, Telegraph Group Ltd
THE STATEMENT
"I was discharged from Salisbury District Hospital on the 9th April 2018. I was treated there with obvious clinical expertise and with such kindness, that I have found I missed the staff immediately.
"I have left my father in their care, and he is still seriously ill. I too am still suffering with the effects of the nerve agent used against us.
"I find myself in a totally different life than the ordinary one I left just over a month ago, and I am seeking to come to terms with my prospects, whilst also recovering from this attack on me.
"I have specially trained officers available to me, who are helping to take care of me and to explain the investigative processes that are being undertaken. I have access to friends and family, and I have been made aware of my specific contacts at the Russian Embassy who have kindly offered me their assistance in any way they can. At the moment I do not wish to avail myself of their services, but, if I change my mind I know how to contact them.
"Most importantly, I am safe and feeling better as time goes by, but I am not yet strong enough to give a full interview to the media, as I one day hope to do. Until that time, I want to stress that no one speaks for me, or for my father, but ourselves. I thank my cousin Viktoria for her concern for us, but ask that she does not visit me or try to contact me for the time being. Her opinions and assertions are not mine and they are not my father's.
"For the moment I do not wish to speak to the press or the media, and ask for their understanding and patience whilst I try to come to terms with my current situation."
