Chris Gard and Connie Yates, who are in their 30s and come from Bedfont, Middlesex, want 10-month-old Charlie Gard, who suffers from a rare genetic condition and has brain damage, to undergo a therapy trial in America.
They have asked European Court judges in Strasbourg, France, to consider the case after exhausting all UK legal options.
Strasbourg judges have said doctors in London should continue providing life support treatment to Charlie until midnight today to give the couple’s lawyers time to submit detailed legal arguments.
Judges were asked to make decisions earlier this year after Charlie’s parents became embroiled in a dispute over treatment with doctors in London.
Specialists at Great Ormond Street Hospital, where Charlie is being cared for, say therapy proposed by a doctor in America is experimental and will not help.
They say life support treatment should stop.
A High Court judge in April ruled against a trip to America and in favour of Great Ormond Street doctors.
Mr Justice Francis concluded that life support treatment should end and said Charlie should be allowed to die with dignity.
Three Court of Appeal judges upheld that ruling and three Supreme Court justices dismissed a further challenge by the couple.
Mr Justice Francis made a ruling after a trial in the Family Division of the High Court in London.
He heard that Charlie, who was born on August 4 last year, had a form of mitochondrial disease, a condition which causes progressive muscle weakness and brain damage.
Specialists in the US have offered a therapy called nucleoside.
Lawyers representing Charlie’s parents say parents should be free to make decisions about their children’s treatment unless any proposed treatment poses a risk of significant harm.
Great Ormond Street doctors may get guidance from a judge on what treatment they should provide if European court litigation progresses.
Lawyers representing Great Ormond Street specialists have raised concern about the parameters…