High Court judge Anthony Hayden rejected an appeal by Tom Evans and Kate James for a delay in turning off their 23-month-old son's life support in order to give them time to present a new challenge.
The ruling allowed doctors at Alder Hey Children's Hospital in Liverpool, northwest England, to withdraw treatment.
Alfie, who suffers from a rare degenerative neurological condition that causes chronic seizures, has been in a coma for over a year and needs a ventilator to keep him breathing.
His parents want to take him to the Bambino Gesu (Baby Jesus) paediatric hospital in Rome which is administered by the Vatican.
Hundreds of people have protested outside the Liverpool hospital in support of the father's plea for the boy to be discharged.
On Monday, a large group of protesters attempted to storm the entrance before being blocked by police.
Evans met with Pope Francis in the Vatican last Wednesday, pleading with him to "save our son" in a Facebook post afterwards.
At his weekly audience the same day, the pontiff drew attention to the case.
"I want to reiterate and strongly confirm that the only master of life, from the beginning to its natural end, is God, and our duty is to do everything to protect life," he said.
Italy granted the toddler citizenship on Monday in a bid to facilitate his transfer to Rome.
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