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 United States and Italy.
The petition and the prospect of US legislation are the latest in a months-long battle over whether Charlie should be taken off life support or receive a new treatment that the hospital has previously said would be futile.
The couple delivered a petition to the hospital of more than 350,000 signatures, calling on doctors at GOSH to allow Charlie to receive experimental treatment overseas.
Charlie inherited the faulty RRM2B gene from his parents, affecting the cells responsible for energy production and respiration and leaving him unable to move or breathe without a ventilator.
Supporters say they will give the hospital a petition signed by 350,000 people backing the parents' rights to take the baby from the hospital for treatment.
Asked how Charlie's parents were feeling, the pro-life advocate said: "They are stressed as anyone would be in this situation, where their own parental rights are being stripped away by an institution that was hired to care for their son and instituted to care for the most vulnerable among us".
"If he's still fighting, we're still fighting", said Connie Yates, the mother of 11-month-old Charlie Gard. Yates and Charlie's father, Chris Gard, spoke outside London's Great Ormond Street Hospital, where the baby is in intensive care and on life support.
Under a High Court ruling, the hospital is forbidden from allowing Charlie to be transferred for nucleoside therapy anywhere.
The U.S. should grant terminally ill Charlie Gard and his parents legal residency so the British baby can undergo trial treatment stateside, a pair of Republican lawmakers argued.
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"Our priority has always been, and will always be, the best interests of Charlie Gard", the hospital said.
But GOSH said its doctors believed the treatment would be "futile" and could prolong the boy's suffering.
Ms Yates added: "If he's still fighting, we're still fighting".
'He's our son, he's our flesh and blood, ' she said. One of those doctors is a researcher and neurologist from Bambino Gesù Children's Hospital in Rome, which has previously offered to treat Charlie. Charlie will die from his illness, his doctors have said.
The hospital said on Friday it would let the courts re-examine claims that he could be treated, citing "fresh evidence" after US President Donald Trump and Pope Francis drew worldwide attention to the case.
Charlie's parents have spoken to the father of Ashya King, a young cancer patient whose parents took him out of hospital and overseas for proton beam therapy not offered on the NHS, The Sun reported.
"Our bill will support Charlie's parents' right to choose what is best for their son, by making Charlie a lawful permanent resident in the U.S.in order for him to receive treatments that could save his life", the two US lawmakers said in a statement.
Lidington said on Sunday that the government won't play a role in deciding Charlie's medical treatment, and that Monday's hearing will be decided by judges acting "independent and dispassionately" based on the facts of the complicated case, according to a report by the Associated Press.
The hospital said in June that if did apply for ethical permission to attempt nucleoside therapy on baby Charlie, but by the time that decision was made, the infant's condition had worsened.