His statement comes two days after he warned North Korea of "total destruction" if its leader Kim Jong-Un, whom he mockingly described as a "Rocket Man", continued with his provocative behaviour.
"We will be putting more sanctions on North Korea," Trump told reporters in response to a question during his bilateral meeting with Afghan President Ashraf Ghani.
North Korea fired a missile over Japan earlier this month and tested a hydrogen bomb, prompting Trump to insist that "all options were on the table" in an implied threat of pre- emptive military action.
The UN Security Council recently held two unanimous 15- to-0 votes adopting hard-hitting resolutions against North Korea, he said.