Prime Minister Jacinda Ardern has thanked an eight-old-year girl for her "lovely note" about banning dangerous guns.

The Dunedin girl, named Lucy, wrote to Ardern telling her she thought it was a good idea to ban dangerous guns from New Zealand.

"Thank you for being our prime minister," the girl said in the hand-written letter.

After receiving the rainbow paper letter, the Prime Minister wrote a personal heartwarming letter back.

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Lucy's mother tweeted a photo of the letter saying: "From the bottom of my heart, and that of my 8-year-old.

Ardern told Lucy that her kind words of support and encouragement had really helped her and praised her.

"I can tell from your letter that you are a kind and compassionate girl, Lucy, and I would just like to encourage you to keep spreading that kindness throughout your life," she wrote.

Ardern also said another thing we could do was show love to our Muslim community, and challenge anybody who is being mean based on somebody's religion, culture or race.

"Together we can make sure that we don't let that kind of hatred grow and turn into violence," Ardern said.