The US president has often spoken fondly of the North Korean leader despite the lack of progress in negotiations to dismantle the regime's nuclear weapons program.
The two spoke for nearly an hour, and Trump became the first sitting president to enter North Korea when he briefly stepped across a military demarcation line that separates the two Koreas.
"Misinterpreting North Korea's situation is risky", 38 North's analyst added.
North Korean chief Kim Jong Un speaks in the course of the 4th Plenary Assembly of the seventh Central Committee of the Employees' Get together of Korea (WPK) in Pyongyang on this April 10, 2019 picture launched on April 11, 2019 by North Korea's Korean Central Information Company (KCNA).
Until earlier this year, North Korea had called for United Nations sanctions, aimed at thwarting its nuclear and ballistic missile ambition, to be lifted, while claiming that it has started to take concrete measures toward denuclearization.
"As the president has said, sanctions will stay on until the final, fully verified denuclearization" of North Korea, the source said.
"(A) freeze, you know, that would never be the resolution of a process", spokesperson Ortagus told reporters.
Beforehand, North Korea's official head of state was the president of the titular parliament, often called the Presidium of the Supreme Folks's Meeting.
According to ANI news reports, if the U.S. plan went ahead, it would see the sanctions' lifting from North Korea's exports of coal and textiles - considered as a major income source for the reclusive communist nation and that it may effort to take denuclearization negotiations back on track after the Hanoi summit failure.
The sanctions suspension could help build trust between the two long-time foes and provide a model that could be expanded as North Korea takes further disarmament steps, Yonhap said, citing the person close to the White House.
Midafternoon, after Yonhap's story on this "potential offer" had been widely reported by worldwide media without being contested, a denial came from State Department spokeswoman Morgan Ortagus.
Ortagus said Washington's goal remained the complete elimination of all of North Korea's weapons of mass destruction.
"President Xi elaborated on China's principled position on the Peninsula issue during his meeting with President Trump in Osaka", Foreign Ministry spokesperson Geng Shuang said at a regular press briefing in the Chinese capital.
But since the Vietnam summit, North Kore has significantly reduced diplomatic activity and exchanges with South Korea and demanded that Seoul break away from Washington and resume inter-Korean economic projects held back by USA -led sanctions against the North.