Connie also told members of "Charlie's Army" that had gathered at the hospital that they had the support of at least seven doctors around the world, including in the USA and Italy.
Chris Gard told reporters Sunday that the USA hospital where they want their son to be treated has doctors who specialize in Charlie's condition.
The two hospitals were not named, but NewYork-Presbyterian Hospital and Columbia University Irving Medical Center said in their own statement Friday that they "have agreed to admit and evaluate Charlie provided that the arrangements are made to safely transfer him to our facility, legal hurdles have cleared and we receive emergency approval from the FDA for an experimental treatment as appropriate".
'He's our son, he's our flesh and blood, ' she said.
The baby's life support was due to be switched off last week, but the hospital delayed in order to give his parents more time with him.
The 11-month-old was born with a rare inherited mitochondrial disease that left him unable to move his limbs or breathe without a respirator.
His family said the fight was not over.
"We believe, in common with Charlie's parents, it is right to explore this evidence", Great Ormond Street Hospital said in a statement Friday.
That prompted the hospital to seek another High Court ruling.
She added: "There is nothing to lose, he deserves a chance".
His defiant mum then announced: 'If he's still fighting, we're still fighting'.
The same day, US President Donald Trump tweeted that the US would be delighted to help the boy.
"Our doctors have explored every medical treatment, including experimental nucleoside therapies". Charlie will die from his illness, his doctors have said.
Charlie's parents want to bring Charlie to the US, where a specialist is willing to offer him an experimental treatment for his rare condition called infantile onset encephalomyopathic mitochondrial DNA depletion syndrome, or MDDS.
An online campaign has raised about $1.7 million to send Charlie to the United States.
But, after a worldwide media storm over the case, global experts presented Charlie's family with new evidence that gave the baby a much higher chance of survival than previously thought.
The petition comes as two USA congressmen have promised to introduce a bill that would give the baby and his parents lawful permanent residency status in the United States, so the boy can undergo treatment in the country.
The hospital said a court should assess the claims of fresh evidence and "make its judgment on the facts".
Doctors finally bowed to global pressure on Friday to give the desperately ill baby another chance.After being handed fresh evidence by seven worldwide experts, Great Ormond Street asked the High Court to reopen the agonising case.