The parents of nine-month-old Charlie Gard say they will keep fighting to get him experimental treatment in the US.
Supreme Court judges have ruled Charlie will be kept on life support until his parents’ appeal can be considered.
“While he’s still fighting, we’re still fighting,” his father Chris told the BBC’s Victoria Derbyshire programme.
Specialists at Great Ormond Street Hospital, in London, say Charlie has irreversible brain damage and should be moved to palliative care.
But his parents Connie Yates and Chris Gard want to take their son to the US for a treatment trial, which they have raised £1.3m to fund.
A legal agreement with the hospital, where Charlie receives 24-hour care, had been due to run out at midnight on Wednesday.
Supreme Court judges said they would consider a further appeal on 8 June.
“He’s fought so hard to be here, he’s still fighting,” Mr Gard said.
“What other option do we have? Charlie is our son, we love him, we will fight to the bitter end for him, and whatever we have to go through to give him the chance he needs, we are more than willing to do.”
Ms Yates added: “It’s literally life or death. If we don’t get this opportunity he’s going to die. He hasn’t got anything to lose. Even if it doesn’t work, which I think it will, we know that we’ve done everything that we can for him. We don’t want to live with the what if?”
Charlie has mitochondrial depletion syndrome, a rare disorder that affects the genetic building blocks that give energy to cells.
Great Ormond Street Hospital said Charlie’s condition had left him unable to see, hear, make a noise or move.
The couple lost their High Court battle in April, when judge Mr Justice Francis concluded life-support treatment should end.
Mr Yates said Charlie was still stable: “He’s putting on weight, his hair’s growing, he’s stable, fighting away, not doing what they said he was going to do.
“We can still take him out for cuddles, he’s in a big bed now so we can get in, put our arms around him and comfort him. He’s pretty weak now muscle-wise, but he’ll still flicker his eyes at us, move his mouth when we stroke his cheeks, he’s still there.”
The Supreme Court judges said an appeal would only be granted on an “arguable point of law”. If successful, a date for a full hearing will be set.
‘Parental rights stripped’
Mr Yates said it was another week of Charlie “just lying there” while he could be receiving treatment.
“We’ve had to stomach the fact they don’t want to do the treatment here, we don’t agree with that but we accept that, but the fact they are blocking us from taking him to another hospital in the world with one of the leading experts in this, I still can’t get my head round it.
“They basically kept him a prisoner there, our parental rights have been completely stripped the moment we took him in there. In hindsight we lost him because they have complete responsibility for him.
“When we got the appeal papers they said Connie Yates and Chris Gard against Great Ormond Street Hospital and Charlie Gard and yet he’s our son. It broke my heart when I saw that because how can that be right?”
A spokesperson for the hospital said: “Both the High Court and the Court of Appeal have decided that it is in Charlie’s best interests for treatment to be withdrawn.
“We have been asked to continue to provide treatment until the Supreme Court meets and we respect that wish.”
Watch the Victoria Derbyshire programme on weekdays between 09:00 and 11:00 BST on BBC Two and the BBC News Channel.