President Donald Trump met with Kim last month but has yet to hold any new talks in his effort to rein in North Korea's nuclear program.
The "Last Week Tonight" comedian roasted the president for being palsy-walsy with "murderous autocrats" after a fresh sexual misconduct allegation.
After becoming the first U.S. president to briefly enter North Korea on Sunday, Trump and Kim agreed during a closed-door meeting to restart nuclear talks.
Speaking to ABC News George Stephanopoulos, the US president stressed his "very strong relationship" with the "very smart" Kim Jong Un.
Talks between the U.S. president and Kim Jong Un abruptly collapsed in Hanoi earlier this year.
The announcement coincided with a moment of discord in efforts by US to reach a deal with North Korea to end nuclear tensions on the Korean peninsula.
The reported launch comes after Kim Jong Un and President Donald Trump failed to reach a deal earlier this year at their second international summit.
Indonesian Siti Aisyah and her Vietnamese co-defendant, Doan Thi Huong, have said they thought they were taking part in a prank for a TV show.