Chris and Connie will now put all their efforts into creating a foundation, where Charlie's voice will "continue to be heard". The hospital sought to remove his life support so he can "die with dignity".
Chris Gard and Connie Yates announced at the High Court that they are no longer fighting with London's Great Ormond Street Hospital (GOSH) to allow him to fly out to the U.S. to receive experimental treatment for Charlie's rare mitochondrial disease.
Judge Francis was due to rule Monday on whether there was sufficient new evidence to permit the parents to bring Charlie to the US for a an experimental therapy.
The couple said they had wanted to give Charlie a real chance of getting better and that a "whole lot of time has been wasted".
Charlie's parents began their fight to send their son to the U.S.in February, when GOSH applied for the High Court to decide whether or not it was legal to fly the infant overseas for therapy.
Over the weekend, the Great Ormond Street Hospital in London revealed its staff had received death threats over the case.
"Sadly the window of opportunity no longer exists".
"It's too late for Charlie", Armstrong said.
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Protesters who wanted Charlie to receive the experimental treatment rallied outside the courthouse, including some who came from as far as the United States.
"Dark days lie ahead for (Charlie's) parents", Mr Armstrong said.
Armstrong said the news had left Charlie's parents extremely distressed and they now "wish to spend the maximum amount of time they have left with Charlie". Charlie was going to be disconnected on June 30, but the Hospital made a decision to give them more time.
The couple's barrister Grant Armstrong said: "This case is now about time".
The parents of Charlie Gard, Chris Gard and Connie Yates, have withdrawn their legal challenge before the High Court in London, England.
In early June, the parents also lost an appeal to the country's Supreme Court, and later in the month, the European Court of Human Rights declined to intervene.
In April, the High Court ruled that GOSH could turn off Charlie's life-support machine.
Gard and Yates wanted to take Charlie-who has a severe condition called infantile onset encephalomyopathy mitochondrial DNA depletion syndrome-to the US because an anonymous physician there had agreed to provide an experimental treatment known as nucleoside therapy.
If Gard and Yates can take comfort at all, it's that their child helped shine a light on the danger of encroaching state prerogative and a parallel utilitarian view of life.
He travelled to London last week to examine Charlie for the first time and discuss the case with Great Ormond Street doctors.