On Monday the couple were given 48 hours to present new evidence as to why Charlie should receive nucleoside therapy in the U.S. for his mitochondrial depletion syndrome, a condition that causes progressive muscle weakness and brain damage.
People gather in support of continued medical treatment for critically-ill 11-month old Charlie Gard due to be taken off life support, in London on Thursday.
He added that it had come to his attention that members of Great Ormond Street had "come under the most vile abuse and threats" from members of the public who have taken up Charlie's cause.
This morning has been an emotional one for the parents of Charlie Gard.
Francis said it was unlikely the hearing would conclude Thursday but said he would consider any new evidence put forth.
As well as, the specialist in the U.S. who was offering therapy, a hospital in Rome had also made an offer, Mr Armstrong said. But, unlike his parents, it does not believe that Charlie can be helped.
Parents of Charlie Gard, Connie Yates and Chris Gard pose for the media ahead of delivering a petition with more than 350,000 signatures to Great Ormond Street Hospital in London, Sunday, July 9, 2017.
The doctor estimated a 10% chance of improvement in muscle strength and a "small but significant" improvement in brain function. If it has not grown, this can be used as evidence of the severity of the baby's brain damage.
Meanwhile, the family's barrister, Grant Armstrong, responded vigorously to a remark by the judge that the proposed treatment has never been tried on mice with Charlie's condition, let alone humans.
Yates interrupted Francis mid-statemen, t while Chris slammed his fist on the table in anger.
"We are continuing to spend every moment, working round the clock to save our dear baby Charlie", they said. And on Sunday, his parents handed in a 350,000-signature petition calling for their son to travel to the USA for treatment.
Roger Kiska who is part of the Legal Council team at Christian Concern told Premier the courts should respect the rights of Charlie's parents.
And, for us here in California, Charlie's case gives us a startling glimpse into the harsh reality of what "single-payer" socialized medicine will look like when decisions about lives and treatment of terminally ill, the elderly, and frail are in the hands of bureaucrats whose primarily duty is to keep the whole system fiscally solvent. Therefore, it's completely unlawful for British courts to rule against them in the first place.
The courts blocked their request on June 30.
But his parents are refusing to give up hope, and have raised around £1.3million to take him to America for treatment. "If he is still fighting, then we are still fighting". Charlie's mother Connie Yates shouted out, accusing Francis of misquoting her earlier statements about her son's quality of life.
US Vice President Mike Pence told "The Rush Limbaugh Show" on Monday that he was praying Charlie's family would "be able to choose the greatest extent of life saving treatment that's available for their child".