He said: "They are hoping to sway the judge to rule in favour of their son's life by granting them permission to seek alternative treatment with medical experts specialising in the disease affecting Charlie - mitochondrial DNA depletion syndrome".
Charlie Gard has a rare genetic condition.
In April, Mr Justice Francis ruled that treating doctors at Great Ormond Street Hospital should be able to turn off Charlie's life support, and said he should not go overseas for further treatment.
Mr Justice Francis has challenged the couple to produce dramatically new evidence that the therapy they want to try in the USA has a chance of working.
Earlier this week, the boy's parents submitted a petition of over 350,000 signatures to the hospital, demanding that they be allowed to take him to the United States for treatment.
At the High Court this morning, Grant Armstrong, acting for the parents, told the judge he had been "in error" when previously assessing key medical evidence in Charlie's case.
The couple now want the High Court judge in London who made the initial ruling to carry out a fresh analysis of their case.
The family lost their legal battle at the end of last month when the European Court of Human Rights upheld the British court's decision that a trip to the United States would cause unnecessary suffering.
Charlie's plight has touched people around the world and the family have received donations totalling more than £1.3 million to take him to the U.S. for therapy.
Mr Justice Francis, who ruled in April that ending life-support treatment would be in Charlie's best interests, said he could potentially revise his decision if "new and powerful" evidence came to light.
However, he warned that he will only consider allowing Charlie to go to therapy in the United States on the basis of new evidence, rather than arguments that have already been dismissed by himself and the Court of Appeal.