US President Donald Trump told South Korea's presidential envoy that Washington was willing to resolve the North Korean nuclear crisis through engagement under the right conditions, South Korea's Yonhap News Agency reported on Thursday.

Trump has said "a major, major conflict" with North Korea was possible and all options were on the table but wanted to resolve the crisis diplomatically and peacefully, possibly through the use of economic sanctions.

South Korea's new President Moon Jae-in who took office last week has campaigned on a more moderate approach toward the North but he has said North Korea must change its attitude of insisting on arms development before dialogue was possible.

Moon's envoy to Washington, South Korean media mogul Hong Seok-hyun, said Trump spoke of the willing to use "engagement" to create peace on the Korean peninsula, Yonhap news quoted Hong as saying.

But the United States will not have any dialogue with the North for the sake of dialogue and the use of pressure was the premise in the approach to Pyongyang, Hong quoted Trump as saying, according to Yonhap.

Trump's comments could not immediately be independently verified.

North Korea conducted its latest ballistic missile test on Sunday in defiance of UN Security Council resolutions, saying it was a test of its capability to carry a "large-size heavy nuclear warhead."

The North has vowed to develop a missile mounted with a nuclear warhead that can strike the mainland United States.

But a senior North Korean diplomat has said Pyongyang was open to having talks with Washington under the right conditions.