"William and I are hugely excited to be in Malaysia. This is our first-ever visit," she said as she began her speech.
The royal couple is on a nine-day tour of the Far East and South Pacific in celebration of Queen Elizabeth II's Diamond Jubilee.
Prince William and Kate arrived in Malaysia after visiting Singapore. They had lunch with Malaysian Prime Minister Najib Razak and other government officials before visiting a hospice in a Kuala Lumpur suburb. While visiting the hospice, Prince William's wife delivered a nearly two-minute speech from a prepared text.
"Providing children and their families with a place of support, care and enhancement at a time of great need is simply life-changing," she said.
Kate is patron of the East Anglia Children's Hospice, a U.K.-based charity. She said she was excited to be learning about Malaysia's first palliative care program for children.
"This is a very special place, and so much is already being achieved," she said. "It has been wonderful meeting the patients, the families and all the staff here. You have given us the most wonderful welcome."
William and Kate spent time talking to young patients and drawing on clay bricks. William drew a cat and mouse that resembled cartoon characters Tom and Jerry, while Kate drew a tree with birds flying above it, according to British Embassy representatives.
The couple is scheduled to visit a Malaysian tropical jungle region on Borneo island before heading to the Solomon Islands on Saturday. They will finish their tour in Tuvalu.
The Associated Press contributed to this report.