Judge Anthony Hayden told a High Court hearing in Manchester, northwest England, that the long-running case had now reached its "final chapter" as he turned down a bid to take the 23-month-old to Italy to continue medical treatment.
Pope Francis had issued an appeal on Twitter Monday that the parents' "desire to seek new forms of treatment may be granted" for the boy, who suffers from a rare degenerative neurological condition.
Italy has previously said it was granting citizenship to the toddler.
The judge said the best they could hope for was to "explore" the options of removing the boy from intensive care either to a ward, a hospice or his home.
Hayden had on Monday rejected another appeal by the parents, Tom Evans and Kate James, for a delay 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.
The boy's father told reporters on Tuesday that the doctors had withdrawn life support on Monday but his son was still alive.
Evans met Pope Francis in the Vatican last Wednesday after several statements of support made by the pope.
"Moved by the prayers and immense solidarity shown little Alfie Evans, I renew my appeal that the suffering of his parents may be heard and that their desire to seek new forms of treatment may be granted," the pope said on Twitter.
At an audience last week, he told attendees in reference 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".
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.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)
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