Pompeo spoke to Trump, national security adviser John Bolton and White House chief of staff John Kelly by secure phone before starting yesterday's session.
He added that the Trump administration was committed to reaching a deal under which North Korea would denuclearise.
Pompeo and Kim met amid growing scepticism over how serious Kim Jong Un is about giving up his nuclear arsenal and translating the upbeat rhetoric following his June 12 summit with Trump into concrete action.
North Korea is Pompeo's first stop on his first around-the-world trip as America's top diplomat.
He will then travel to Japan, Vietnam and the United Arab Emirates before heading to Belgium, where he will accompany Trump at the Nato summit in Brussels.
Yesterday the Washington Post reported Trump will land in Europe this week amid fears that he will blow up a key summit focused on Europe's defence and then offer concessions to Nato's main adversary, Russian President Vladimir Putin.
The allies' worries and Moscow's hopes are rooted in Trump's combative approach to foreign policy.
In recent days, Trump has told senior aides that he wants to slash US spending on Europe's defence if the allies are unwilling to contribute more to Nato, a senior official said.
The private comments reflect a president who has shown little interest in the long history that undergirds America's alliances or the collective foreign policy expertise of the US Government, according to current and former US and European officials.
Instead, he relies on his instincts and his ability to forge a personal bond with world leaders.
But his approach has also heartened autocrats, such as Putin, who see in Trump someone willing to forgive past sins in pursuit of a deal, the officials said. And it has alarmed allies and some of Trump's closest aides, who are concerned he may yield on issues such as Russia's annexation of Crimea and its continuing destabilisation of Ukraine.
Even as his Administration has imposed tough sanctions on Moscow and expelled Russian diplomats, Trump has avoided criticising Putin. He will meet Putin in Helsinki on July 16.
- AP, Washington Post