Quoting former US officials familiar with the trips, the Los Angeles Times said the brief visits in April and August 2012 were aimed at encouraging the new leader to change the foreign policy after the death of his father Kim Jong Il.
However, the Communist state leadership apparently spurned the outreach effort, the paper said.
The first visit in April was led by Joseph DeTrani, a North Korea expert who then headed the National Counter Proliferation Center in the Office of the Director of National Intelligence, the officials said.
North Korea carried out the launch on April 12. The missile flew only a few minutes before it exploded. A subsequent test in December was successful.
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It was unclear who led the August trip.
The paper quoted them as saying that Sydney Seiler, who is in charge of Korea policy at the National Security Council, went on both trips. Seiler, a veteran CIA analyst, speaks fluent Korean. He could not be reached for comment.
The White House, the State Department and the CIA have refused to confirm or deny the 2012 trips, the paper said.
News of the secret trips first leaked out in the South Korean press, which said the flights from Guam to the Sunan airport in Pyongyang, North Korea's capital, passed through South Korean airspace.
"The South Korean air force was tracking the plane. They knew there was a special flight going to Pyongyang, but the purpose of the mission was a secret," said Moon Chung-in, a former South Korean government advisor on North Korea.
US officials have visited N Korea on and off for years. The last official US visit was in 2009 when special envoy Stephen Bosworth sought to restart stalled six-party talks on North Korea's nuclear programme. The talks have not resumed.