Meetings were also held this week with Charlie's mother, doctors treating Charlie at Great Ormond Street Hospital and American specialist Dr. Michio Hirano, an American neurology expert from Columbia Medical Center in NY who has designed the experimental treatment.
Mr Justice Francis has considered the latest stage of the case at public hearings in the Family Division of the High Court in London.
His parents are fighting to get him more medical care but Great Ormond Street Hospital has said the experimental treatment will not work and will just cause more suffering.
A judge at the High Court has been hearing evidence about the potential of an experimental treatment that it is claimed could help the baby.
Eleven-month-old Charlie has an extremely rare genetic disorder, mitochondrial depletion syndrome, that causes progressive muscle weakness and brain damage.
The 10-month old baby was born "perfectly healthy" on August 4, previous year but around a month later his parents Chris Gard and Connie Yates noticed that he was less able to lift his head and support himself in comparison with other babies of a similar age.
"In recent weeks the GOSH community has been subjected to a shocking and disgraceful tide of hostility and disturbance".
"Despite conflicting issues, we have always had the utmost respect for all the staff who work tirelessly at Great Ormond Street Hospital and the very hard jobs they do every day".
In a statement, the hospital said police had been called to investigate the "shocking" threats and "unacceptable" harassment of staff - which has included abuse in the street as well as online messages.
The court is expected to rule next week whether or not 11-month old Charlie can be taken to the U.S. for experimental treatment. Staff have received abuse both in the street and on line.
Charlie's parents have, however, received support from Pope Francis, U.S. President Donald Trump and some members of the U.S. Congress.
British and European courts have so far backed the doctors' position, ruling that transferring Charlie to the USA would prolong suffering without a realistic prospect of success.
"We fully understand that there is intense public interest, and that emotions run high", she said in Saturday night's statement.
The court is due to hold a hearing on Monday to consider the latest medical evidence.
Charlie's mother spent this week meeting with doctors at the hospital and the American specialist, Michio Hirano, according to the Associated Press.