"If we can help little #CharlieGard, as per our friends in the U.K. and the Pope, we would be delighted to do so," he said in a tweet.
The parents of Charlie Gard, who is 10 months old and has brain damage, had been fighting to take him to the United States for an experimental treatment for his extremely rare form of mitochondrial disease but lost their case in British courts and the European Court of Human Rights.
The baby's plight has also attracted the attention of Pope Francis, who on Sunday expressed his support for Chris Gard and Connie Yates, saying he hoped doctors would allow them to "care for their child until the end."
The Italian term used -- "curare" -- can be translated as "care for" or "treat" but the Vatican press office could not provide an official translation into English.
Trump's offer of intervention was met with both support and criticism on social media. Some hailed him as a "pro-life president" and decried what they termed the pitfalls of public-funded health care in Europe.
But others accused him of wading uninformed into a complex issue, and slammed his offer of medical help to Charlie amid a bruising legislative fight over health care in the United States.
Charliesfight.org, a page set up to solicit donations for the baby's treatment in the United States, noted, "Two of the most powerful men in the world want to give Charlie Gard his chance," while @Fight4Charlie, an associated account, responded: "Thanks @realDonaldTrump for your support - @teresamay do the right thing and #savecharliegard."
The case has tugged at heart strings in Britain, where more than 1.3 million pounds ($1.6 million) has been raised through GoFundMe to pay for the experimental treatment.
A hundred protesters held a demonstration outside the gates of Buckingham Palace in London on Sunday, shouting "Save Charlie Gard" next to a banner that read "Murder."
Great Ormond Street Hospital for Children in London, which has been treating Charlie, issued a statement on Friday following the European court's decision which did not specify when life support would be removed.
"Together with Charlie's parents we are putting plans in place for his care, and to give them more time together as a family," it said, asking for privacy for the baby's parents.
The courts had ruled that keeping the baby on life support would only prolong his suffering as there was no hope of his recovering from the disease which causes progressive muscle weakness, including in key organs such as the heart.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)