Bosworth held talks with several senior North Korean officials but did not meet Kim himself.
Speaking to the Associated Press, an unnamed state department official said the contents of the letter followed the general message that Bosworth had taken to Pyongyang.
"The North Koreans have a choice: continued and further isolation or benefits for returning to the six-party talks and dismantling their nuclear weapons program," the official said.
Bosworth's talks were the Obama administration's first high-level contact with North Korea.
Speaking after the visit he said the two sides had reached a "common understanding" on the need to restart the nuclear negotiations.
The six party talks, aimed at denuclearising the Korean peninsular, involve the two Koreas, China, Japan, the US and Russia.
|North Korea pulled out of the nuclear disarmament talks in April [AFP]
Former US presidents George Bush and Bill Clinton both also sent personal letters to Kim, raising the benefits of disarmament.
Bush wrote to Kim in December 2007, offering normalised relations if the North
Korean leader fully disclosed his nuclear programs by year's end.
The letter was seen as a turnabout for a president who had labelled the secretive regime part of an "axis of evil", along with Iran and pre-war Iraq.
According to the Washington Post, efforts early in Bush's term to send a letter were stymied by an intense debate over whether to use an honorific such as "his excellency" to address Kim.