Pope Francis, who met Mr Evans after he flew to Rome, said on Twitter: "I am deeply moved by the death of little Alfie.
"Today I pray especially for his parents, as God the Father receives him in his tender embrace."
The family of Alfie Evans said they have been left "shattered" by his death, as more than 1,000 supporters gathered to release balloons in his memory.
The terminally ill 23-month-old, who was being treated at Alder Hey Children's Hospital in Liverpool, died at 2.30am on Saturday, his parents Kate James and Thomas Evans said.
Hundreds gathered in Springfield Park, next to the hospital, to release blue and purple balloons in his memory at 2.51pm - exactly 12 hours after he was officially pronounced dead.
Mr Evans and Ms James, both in their early 20s, did not attend the event but Mr Evans's sister Sarah told the crowd: "I just want to thank you all for coming today. Our gorgeous little warrior took his last breath at 2.30 this morning.
"Our hearts are broken. We are absolutely shattered as a family.
"Thomas just wants to thank you all for the support you've all shown. There's only one Alfie Evans."
She said the family had hoped to bring the youngster home on Saturday.
Announcing the death of Alfie, who has been at the centre of a court battle over whether to withdraw life support treatment, his mother wrote on Facebook: "Our baby boy grew his wings tonight at 2:30am. We are heart broken. Thank you everyone for all your support."
In a post on his own Facebook page, Mr Evans said: "My gladiator lay down his shield and gained his wings at 02:30. Absolutely heartbroken. I LOVE YOU MY GUY."
Flowers, cards and toys were left outside the hospital as supporters came to pay their respects.
One card said: "We fell in love with a little boy we never knew. Alfie will be forever engraved in our heart. Fly high little man."
A spokesman for Alder Hey said: "We wish to express our heartfelt sympathy and condolences to Alfie's family at this extremely distressing time.
"All of us feel deeply for Alfie, Kate, Tom and his whole family and our thoughts are with them.
"This has been a devastating journey for them and we would ask that their privacy and the privacy of staff at Alder Hey is respected."
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