The European Court of Human Rights has rejected a plea from the parents of a terminally ill British baby to intervene in the case.
Charlie Gard has a severe mitochondrial condition and in January suffered what doctors describe as irreversible brain damage.
Specialists at Great Ormond Street Hospital think the 10-month-old has no chance of survival and want to end his life support treatment.
But his parents, Chris Gard and Connie Yates, from Bedfont, west London want him to undergo a therapy trial in the US.
On 19 June, judges at the ECHR ordered doctors to continue treatment while they considered the complex case.
But they have now announced the application by Charlie's parents is "inadmissible".
The European Court announced that it had by a majority "endorsed in substance" the approach by the UK courts.
It added that the court "also considered that it was appropriate to lift the interim measure" which had required doctors to continue providing life support treatment to Charlie.
Great Ormond Street said there would be "no rush" to change Charlie's treatment "and any future treatment plans will involve careful planning and discussion".
"Our thoughts are with Charlie's parents on receipt of this news that we know will be very distressing for them.
"Today's decision by the European Court of Human Rights marks the end of what has been a very difficult process and our priority is to provide every possible support to Charlie's parents as we prepare for the next steps."
A High Court judge ruled against Charlie's family in April, a decision backed by the Court of Appeal and the Supreme Court.
The ECHR said the British courts had concluded "on the basis of extensive, high-quality expert evidence, that it was most likely Charlie was being exposed to continued pain, suffering and distress and that undergoing experimental treatment with no prospects of success would offer no benefit, and continue to cause him significant harm".