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6 year oldInterviewed by ABC News, he said North Korea must take "irreversible" steps to get rid of its nuclear arms programme.
Mr Pompeo met Mr Kim secretly in Pyongyang earlier this month as CIA director. Details only emerged later.
Mr Trump is expected to meet the North Korean leader next month to discuss denuclearising the Korean peninsula.
Mr Pompeo said Mr Trump had clearly told him to raise the issue of a verifiable mechanism to make sure North Korea does denuclearise. He also raised the topic of US citizens held by the North Koreans.
Separately, new US National Security Advisor John Bolton told Fox News that an agreement with Libya on eliminating its weapons of mass destruction programme could serve as a model for a North Korea deal.
Libyan leader Muammar Gaddafi agreed with Western powers in 2003 to dismantle his programme in return for the lifting of sanctions.
"There are obviously differences. The Libyan programme was much smaller, but that was basically the agreement that we made," Mr Bolton said.