“As long as there’s no testing, I’m in no rush,” the president said.

With little more than a week to go before the Hanoi meeting, United States and North Korean officials planned to meet in the Vietnamese capital this week to negotiate a potential deal, to be announced by their leaders next week.

Among possible incentives it can offer, Washington has studied exchanging liaison offices with Pyongyang and declaring an end to the 1950-53 Korean War, which was halted in a truce, according to South Korean officials familiar with United States-North Korean talks.

North Korea’s top priority is the easing of economic sanctions. But Washington is reluctant to lessen its economic pressure on the North because doing so would weaken the strongest leverage it has to force the country to rid itself of nuclear weapons.

On Tuesday, Mr. Moon appeared to suggest that if Washington could not immediately ease United Nations or bilateral sanctions, it should consider letting South Korea press ahead with inter-Korean collaborative projects, such as the relinking of railways of the two Koreas, as an alternative incentive for the North.

North Korea has wanted those projects.

During his New Year’s Day speech, Mr. Kim called for the reopening of the joint inter-Korean factory park in the North Korean city of Kaesong, as well as South Korean tours to the North’s Diamond Mountain. The Diamond Mountain and Kaesong projects had provided badly needed foreign currency for the impoverished North until they were shut down in 2008 and 2016, amid rising tensions between the two sides.

Mr. Moon supports broader inter-Korean economic cooperation, arguing that it will help encourage the North to denuclearize by demonstrating the potential economic benefits.

But to promote those projects, South Korea needs exemptions from international sanctions that ban investments, joint ventures and other significant economic cooperation with the North. Until now, Washington has been reluctant to help South Korea win such exemptions, insisting that it refrain from joint economic projects until the North takes important steps toward denuclearization.

Mr. Moon’s critics, including conservative South Koreans, say that an easing of sanctions will only encourage North Korea to drag its feet over denuclearization. They also warn that any exemptions would undermine Washington’s own international efforts to enforce sanctions. China and Russia are already calling for easing the economic restrictions around North Korea.