They got few new clues on Wednesday.

The joint statement that the men signed on Tuesday contained vaguely worded commitments to “complete denuclearization,” “new” relations between their countries and a “peace regime” on the peninsula. In many ways, it was a rehash of agreements that the two nations had reached in the past but never honored.

Only after the signing ceremony did it emerge that more commitments had apparently been made. In a post-summit news conference on Tuesday, Mr. Trump announced that the United States would end joint military exercises with its South Korean allies, which Pyongyang has long denounced as rehearsals for an invasion of the North. The news appeared to catch both the South Korean government and the United States military off guard.

On Wednesday, the office of President Moon Jae-in in Seoul appeared to endorse Mr. Trump’s decision. “While North Korea and the United States are engaged in sincere talks on denuclearization and relations-building, we recognize the need to find various options to smooth such dialogue,” said a spokesman, Kim Eui-kyeom.

Also on Wednesday, the North’s official Korean Central News Agency reported that Mr. Trump had agreed to “lift sanctions” once bilateral relations improve. Mr. Trump had said on Tuesday that the sanctions would stay in place until North Korea dismantled enough of its nuclear program to make it difficult to reverse course. Mr. Trump said the denuclearization process would begin “very soon” and happen “very quickly.”

But the North Korean news agency said the two leaders had agreed to a phased process in which Pyongyang would bargain away its nuclear arsenal in stages, securing reciprocal actions from the United States at each step. Such a process has been opposed by American hard-liners like John R. Bolton, now Mr. Trump’s national security adviser, who has argued in the past that the North must quickly dismantle and ship out its nuclear weapons program in its entirety, as Libya did more than a decade ago.