After holding a working lunch, the two leaders plan to sign a joint statement around 2 p.m.

The contents of the "Hanoi Declaration" is the name of the game.

It remains uncertain whether their deal will contain Pyongyang's plans for concrete denuclearization steps and Washington's reciprocal measures.

Kim could seek to trade the shutdown of the Soviet-era Yongbyon nuclear complex for Trump's declaration of a symbolic end to the 1950-53 Korean War and some sanctions relief if possible.

Speaking to reporters about the possibility of an end-of-war declaration during a Wednesday meeting with Kim, Trump said, "We'll see."

The North's state media reported that the leaders are eyeing a "comprehensive and epoch-making" accord.

"Sincere and deep opinions were exchanged with a view to making comprehensive and epoch-making results in the talks in order to meet the interest and expectation of the whole world for the successful Hanoi summit," the Korean Central News Agency said, referring to their first-day meeting that lasted around two hours and 20 minutes.

Trump also plans to brief reporters in person on the outcome of this week's bargaining with Kim before heading back to Washington on Thursday evening. (Yonhap)