Doctors have been told to continue providing life-support treatment to a terminally ill baby at the centre of a high-profile legal battle for another three weeks to give judges in the European Court of Human Rights time to analyse the case.

Chris Gard and Connie Yates want 10-month-old Charlie Gard, who suffers from a rare genetic condition and has brain damage, to undergo a therapy trial in the US.

Specialists at Great Ormond Street Hospital for Children in London, where Charlie is being cared for, say therapy proposed by a doctor in the US is experimental and will not help.

Chris Gard and Connie Yates with their terminally ill baby son Charlie GardChris Gard and Connie Yates with their terminally ill baby son Charlie Gard

They say life support treatment should stop.

Charlie’s parents hope judges in the European Court of Human Rights, in Strasbourg, France, will come to their aid after losing battles in the High Court, Court of Appeal and Supreme Court in London.

Their lawyers on Monday filed detailed legal arguments and Strasbourg judges say they will treat Charlie’s case with the “utmost urgency”.

Supreme Court justices in London say Great Ormond Street specialists should keep providing life-support treatment until midnight on July 10.

Chris Gard after Supreme Court justices dismissed the couple's challenge (David Mizoeff/PA)Chris Gard after Supreme Court justices dismissed the couple’s challenge (David Mizoeff/PA)

Three justices had analysed issues relating to continued treatment, pending a decision by European court judges, at a hearing in London early on Monday.

A European Court of Human Rights spokeswoman said the case would get “priority”.

“In light of the exceptional circumstances of this case, the court has already accorded it priority and will treat the application with the utmost urgency,” she added.

“It is anticipated that as soon as the responsible chamber of the court is in a position to consider the application made on behalf of Charlie Gard and his parents an expedited timetable for the determination of this application will be established.”

Supporters outside the Supreme Court Supporters outside the Supreme Court on June 8 (David Mizoeff/PA)

A High Court judge in April ruled against a trip to America and in favour of Great Ormond Street doctors.

Mr Justice Francis concluded 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, has 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.