Theresa May has promised a health minister will look into the case of a baby given weeks to live.
Labour MP Emma Lewell-Buck asked the PM to help raise "awareness to find a heart for little baby Carter".
Responding to the comment during Prime Minister's Questions Mrs May said Carter's story was a "tragic case" and she highlighted the new "opt-out" organ donation system due in 2020.
Speaking to the BBC earlier this week, Chris Cookson spoke of his wife's "courage" to carry another baby after saying "goodbye" to Charlie, who died of an undiagnosed condition unrelated to Carter's.
His condition caused muscle and bone problems and compromised his immune system.
"It's taken five years to even think about trying for another child," Mr Carter said.
He described Carter's illness as being "thrown right back in the deep end again".
"We've just got to pray... we can get a heart and we can maybe take our son home and have a life that we didn't have with Charlie," he said.
The Charlie Cookson Foundation supports families of children with life-limiting illnesses.
Ms May commended the family for their charity work and said the "sympathies of the whole house are with the family at this very, very difficult time".