Tom Evans and Kate James lost an appeal Wednesday after a British Court of Appeal upheld a ruling preventing the 23-month old from traveling overseas following the withdrawal of his life support.
The 23-month-old British toddler, who is suffering from a rare undiagnosed degenerative neurological condition, confounded doctors' expectations when he continued to live after his life support was switched off on Monday night, according to reports.
The NHS and Alder Hey's hospital medical staff said that Evans' condition is irreversible and that he should be taken off life support.
The Court of Appeal upheld a ruling on Wednesday preventing the 23-month-old from travelling overseas after life support was withdrawn.
The parents of Alfie Evans have asked to be left alone after their final court appeals failed.
"The court has just heard that Alfie's dad Tom Evans started private prosecution to have three doctors charged with conspiracy to murder yesterday", ITV News reporter Alan Jenkins tweeted (see below).
However, his father, Tom, 21, appealed to the family's many supporters to step aside and allow them to "form a relationship" with Alder Hey Children's Hospital and go on to "build a bridge and walk across it".
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Mr Evans said: "Alfie doesn't need intensive care any more".
The months-long legal battle between Alfie's parents, backed by a Christian pressure group, and his doctors has drawn interventions from the pope and Italian authorities, who support the parents' desire to have their son treated in Italy.
On April 25, the Court of Appeal upheld the High Court decision. On Wednesday he said Alfie was being given food again after 36 hours without it.
His parents, Tom Evans and Kate James, from Bootle, Merseyside, have been fighting against the hospital's wish to have his ventilator switched off.
Polish President Andrzej Duda demanded over Twitter Alfie be saved.
"That must be enough for you now to consider that Alfie may prove you wrong".
Italy has a military plane on standby to transport Alfie to Rome if the courts allow it. Alfie has also been granted Italian citizenship to facilitate his arrival and transport.
Police remained outside the hospital on Thursday, after supporters of the parents have been massing in recent days to protest.
The doctors' letter also called on the General Medical Council to investigate the actions of the staff at Alder Hey Children's Hospital in Liverpool.