Connie Yates spoke after the pope said the baby's parents should be allowed to "accompany and treat their child until the end".
She also acknowledged the support of Donald Trump, who tweeted on Monday: "If we can help little #CharlieGard... we would be delighted to do so."
In a statement, Ms Yates said: "The support from the Pope and the President has given us hope. They are traditional men who believe in the family.
"They believe in our case and understand why we believe it is right to continue fighting so hard to save Charlie."
Connie Yates and Chris Gard want to take Charlie to America for trial therapy. They have been at the centre of a high-profile legal battle with doctors at Great Ormond Street Hospital (GOSH) who believe his life-support care should stop.
Judges in the High Court, the Court of Appeal and the Supreme Court all ruled in favour of GOSH doctors. The European Court of Human Rights refused to hear the family's appeal.
In a further intervention by the Holy See, the Vatican's children's hospital asked GOSH whether the baby could be transferred to Rome for care.
Bosses at Bambino Gesu hospital (pictured above) say they were told the transfer would not be possible unless the Supreme Court in London agreed.
Foreign Secretary Boris Johnson expressed his support on Wednesday for GOSH, says it was "right that decisions continued to be led by expert medical opinion, supported by the courts".
During a schedule telephone conversation with his Italian counterpart Angelino Alfano, he also stressed that the course of action should be "in line with Charlie's best interests".
Charlie suffers from a rare genetic condition and has brain damage. His parents are now spending the final days of his life with him.