By Kris Jepson

Exclusive: Carter Cookson's parents have told ITV News Tyne Tees they hope more people will join the organ donation register in his memory.

Speaking for the first time since their three-week-old son died on Saturday, the couple said they want Carter's legacy to be one that saves lives in the future.

Carter's mum, Sarah Cookson from South Shields told ITV News "when people are in this position or when they're just sitting and it pops up on their feed and it's like 'organ donation, have a think about it', I just hope that they picture his little face and think, that little boy could still be here if there was more people on that donation register".

Watch @krisjepson's report here:

Carter Cookson passed away at the Freeman Hospital in Newcastle on Saturday, following a three week campaign appealing for a new heart.

He was born on Boxing Day, but suffered three cardiac arrests just hours after his birth. He was fitted with a pace maker, but did not respond to emergency surgery.

He needed a heart transplant and his parents appealed to the nation to raise awareness of his plight, but to no avail.

On Saturday, the machine Carter was relying on to pump blood around his body needed changing again, but his body was weak and he passed away.

It took us a few minutes and I think we had some time on our own. We both knew that he was too weak and we had to make a decision to let him go and that kills you. It’s a horrible, horrible thing to do, but you’ve just got to keep thinking you’re doing the right thing by your child. In the end there was just me and Sarah there. We had the songs on that he liked and we were talking to him about things he was going to do with his brother. We told him he’s going to go to a better place and one day that we would see him again.

Chris Cookson, Carter's Dad
Carter Cookson Credit: Family photo

The couple had less than a month with their newborn child and between speaking to the press to raise awareness he needed a new heart, and their son receiving treatment from staff at the hospital, they tried desperately to make memories with Carter.

My first cuddle, because in my eyes, even though there was all the tubes and things there, it was still my first one. We tried to make it as positive as we could and Chris would be telling me off for doing his massaging. We loved the music. We’d been playing all the music that he’d been listening to in my belly for so long and things like that, we just thought, the time will come for us to cry, we need to be strong for him.

Sarah Cookson, Carter's Mum
Carter Cookson Credit: Family photo

When Carter passed away at 5.44pm on Saturday, the couple were in no doubt about what they had to do.

They say they knew he had helped people and his legacy had already started, but they wanted to reiterate their stance on the importance of organ donation.

We both said straight away if we don’t win this battle, we will offer Carter’s organs out to save another baby’s life and we did and when we were asked that question, there was no hesitation at all.

Chris Cookson, Carter's dad

Unfortunately there were no babies the same size as Carter at that point in time who needed his organs and that is something that has saddened his mother.

I would have loved a piece of Carter to continue in another baby because it’s just a little bit easier for us to continue, knowing that a part of him is in another child.

Sarah Cookson, Carter's mum
Carter Cookson Credit: Family photo

Carter's story has grabbed the attention of millions of people across the country and the rest of the world.

Even the Prime Minister spoke in Parliament about his fight for a new heart and organ donation.

South Shields Vigil Credit: ITV News

It was the support from their home town of South Shields that really touched the couple.

Sarah said "The messages of support and their generosity and their kindness has just been so overwhelming, you know, we’ve got a lovely town in South Shields that always get behind times of sadness, but to get messages from New Zealand and Australia and everywhere..."

It’s phenomenal, it’s a phenomenal town. The support is absolutely amazing and I don’t think we would have had the strength to battle through this without all the messages and the heartfelt comments that have been coming towards us.

Chris Cookson, Carter's Dad
Charlie Cookson Credit: ITV News

Carter's unexpected and devastating heart problems came as the cruelest of blows for the Cooksons, who lost their first son Charlie in 2013 when he was just two-and-a-half.

After Charlie’s death, the couple set up the Charlie Cookson Foundation in a bid to support other families with seriously ill children.

For a dad and a mam to hear two South Shields brothers have made a huge difference, you know, just makes, it makes you so proud and you think the deference Carter has made to organ donation, I’m in awe of a boy who was only three weeks old. He’s made me into a stronger person now.

Chris Cookson, Carter's Dad