"If we can help little #CharlieGard, as per our friends in the UK 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.
"Although the president himself has not spoken to the family, he does not want to pressure them in any way, members of the administration have spoken to the family in calls facilitated by the British government."
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."
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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.
The case has tugged at heart strings in Britain, where more than 1.3 million pounds ($1.68 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."