The parents of terminally-ill baby Charlie Gard have been told to spell out fresh evidence which might persuade a judge to let them take their child abroad for treatment.
Chris Gard and Connie Yates, who are in their 30s and come from Bedfont, west London, want 11-month-old Charlie, who suffers from a rare genetic condition and has brain damage, to undergo a therapy trial in America.
Specialists at Great Ormond Street Hospital in London, where Charlie is being cared for, have said therapy proposed by a doctor in America is experimental and would not help.
Great Ormond Street doctors say life-support treatment should stop.
Charlie's parents asked European court judges in Strasbourg, France, to consider their claims after losing battles in the High Court, Court of Appeal and Supreme Court in London. But Strasbourg judges have refused to intervene.
The couple want a High Court judge to make a fresh analysis of their case.
Mr Justice Francis, who ruled in April that Charlie should be allowed to "die with dignity", has overseen a preliminary hearing in the latest round of litigation at a hearing in the Family Division of the High Court.
He said he would consider new evidence but not rake over old facts. The judge said Charlie's parents should outline any new evidence they had and he would oversee another hearing on Thursday.
Lawyers representing Great Ormond Street bosses told Mr Justice Francis on Monday they were struggling to find any new evidence.
Charlie's parents interrupted the hearing and aired concerns directly to the judge.
Ms Yates told the judge: "He is our son. Please listen to us."
Mr Gard yelled at a barrister representing Great Ormond Street bosses, saying: "When are you going to start telling the truth?"
Lawyers representing Charlie's parents said evidence indicated a "small chance" of brain recovery.
They said Charlie's case involved "cutting edge genetic science".
Lawyers said there was a "good prospect" of further evidence producing a different result.