The 42-year-old told Pauline Thomas, 74: “It’s good news but there is still a long way to go” as he took the cards and said “thank you very much” and “very much appreciated”.
Royal fan Sandra Peters, 79, said: “I told him, Bore da, you have a beautiful family, I’m so pleased Kate is recovering. He said thank you very much. He was lovely – he’s so charming.”
She and her friend, Jane Stoneman, 61, both gave him letters to pass on to the Princess. Mrs Stoneman said: “He’s so handsome and beautiful. We’re so lucky to have him.”
The Prince also revealed he had Duolingo, the language learning app, and was trying to learn Welsh “phonetically”.
His Wales trip came fewer than 24 hours after the Princess of Wales, 42, said in an intimate family video message that she had completed her course of chemotherapy after an “incredibly tough” nine months.
She said she planned to make a gradual return to royal duties, but that her focus was on remaining “cancer-free”.
Diane Griffiths, who did not want to give her age, told the Prince: “It was so good to see Catherine looking well – you have a beautiful family.”
She said he had replied, in Welsh, “Diolch”, meaning thank you.
Among those who the Prince met was 10-year-old winner Ruby Davies, whose joyful reaction following her triumph at the Welsh language youth festival went viral.
She gave the Prince some friendship bracelets she had made for his children.
“That’s so sweet,” he told her. “Did you put them together yourself? They’re going to wear those, you’ll see them out and about.”
He added: “I’ll keep them away from Louis because he’ll try and steal all his sister’s bits.”
The Prince told Ruby he had watched her video “several times”, adding: “Charlotte loves her performing and dancing as well, so I’m going to show her your video when I get home.”
The visit was the first of three engagements the Prince is undertaking in South Wales on Tuesday to celebrate Welsh sport and culture.
Still sporting his summer beard, he received a warm welcome on arrival in the school hall, where the children cheered loudly and waved Welsh flags.
“Good morning,” he said, waving to everyone, before spotting Ruby at the front. “There’s Ruby!” he exclaimed, before watching her perform.
During one exchange with the children, a pupil remarked that the Prince had a “bug” on his clothes, prompting the Prince to pass the insect to him and say: “Good spot.”
Urdd Eisteddfod is an annual event that was held this year in Meifod, Powys, at the end of May.
Organised by the National Voluntary Youth Organisation, it involves activities including art, music composition, drama, sport, dancing, singing and reciting for children and young people aged between 8 and 25.
Ruby won the individual reciting competition for Welsh learners in Years 5 and 6, and her excitement afterwards was plain to see.
Chatting to presenter Mari Lovgreen in front of an audience including family members, she declared: “I’m so happy! I love performing as well.”
Lovgreen said: “Well, you’re very good at it,” to which she replied: “Yes, I am.”
Ruby could not understand the presenter’s various responses in Welsh, admitting at one stage: “I don’t know what you’re saying.”
“The best in Wales,” she was told, to much laughter, before echoing the sentiment with a huge smile: “The best in Wales!”
Prince William watched a showcase of the school’s entries before meeting Ruby, her mother Lynne Davies and performers and teachers to hear about the impact of the festival.
Ruby said she wanted to be on the stage when she grew up.
“I’ve got lots of options,” she said ahead of the Prince’s arrival. “I may be a presenter, an actor, a dancer, a singer … I don’t know. But definitely on stage.”
Lynne Davies said she had first learnt the poem she performed, Siopa by Sali Ann Preston, by rote but did not understand its meaning.
“She was just saying words, and I asked her if she understood the meaning and she said ‘no’,” she added. “So we translated it as best we could and then she was able to perform it with expression.”