A lawyer representing Tom Evans, 21, and Kate James, 20, on Monday returned to the Court of Appeal to ask judges to rule that Alfie Evans should be allowed to travel to a foreign hospital.
A United Kingdom judge denied an appeal from Alfie Evans' parents Monday to have him treated outside the country, saying their parental rights did not matter.
In February, Mr Justice Hayden ruled that doctors at Alder Hey Children's Hospital in Liverpool could stop treating Alfie against the wishes of his parents following hearings in the Family Division of the High Court in London and Liverpool.
Appeal court officials said an appeal court judge had decided that Alfie should continue to receive treatment pending the outcome of Monday's Court of Appeal hearing.
Roger Kiska, legal counsel at Christian Legal Centre, told CBN News last week the parents have the legal right to remove Alfie from Alder Hey Children's Hospital.
"There is a passion out there", Mr Diamond told appeal judge Lord Justice Davis, Lady Justice King and Lord Justice Moylan.
She said: "Take it to a neutral ground so there is no impact upon other children, families or staff and they would gain a lot more respect for the cause".
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The next phase is a battle over the procedures involving who may review the materials seized by FBI investigators last week. All the same, this legal back and forth over the potential review, she added, is "highly, highly unusual".
After the High Court judge upheld his original December 2017 ruling that backed Alder Hey doctors in their decision to switch off the toddler's life support, on Thursday night, supporters gathered at the hospital to protest.
It has also been suggested that Alfie was being unlawfully detained or "deprived of his liberty" at Alder Hey.
Alfie's parents say their son has improved in recent weeks and had asked Mr Justice Hayden to allow a new assessment. The court stayed the removal of Alfie's life support, pending the decision of the Supreme Court.
He then alleged the hospital called the police to prevent him removing his son, with officers allegedly telling him he would be "arrested for assault" if he attempted to remove Alfie. Moylan argued, however, that both Bambino Gesu staff and staff at Alder Hey agree that no hope remains for curative or preventative treatment for Alfie and that he should receive end of life care.
However, Alder Hey said in a statement: "Noise from recent protests has unfortunately affected our patients so we would ask that noise levels outside the hospital are kept to a minimum and, for example, vehicle horns are not sounded". The judge said the unanimous view of medical experts was that Alfie's brain had been eroded by disease and further assessment was pointless.
Police are now entering Alder Hey hospital as a crowd of protesters gathers outside chanting "save Alfie Evans!"