His remarks came a day after education secretary Betsy DeVos was criticised for defending a proposed $17.6m (£13.5m) cut to the organisation, which is designed for disabled children.
The request was included in Mr Trump's $4.75tn federal budget, which was not expected to pass Congress.
Mrs DeVos responded she had pushed for funding "behind the scenes".
"I heard about it this morning. I have overridden my people. We're funding the Special Olympics," Mr Trump said of the world's largest sport organisation for people with intellectual disabilities.