Mr Trump made the announcement as he also appeared to blame his predecessor Barack Obama over the death of Otto Warmbier, 22, the United States student who died after being imprisoned for 17 months in North Korea.
Trump says, "Lot of bad things happened but at least we got him home to be with his parents".
Analysts said anger over Warmbier's death would dim, if not scuttle, any prospect of a less antagonistic relationship in the near future between Washington and Pyongyang, which is still holding three other Americans.
The Chinese "have limited capacity to do something, and I think they feel the weight of expectations beginning to burden them", said Christopher Hill, who led the USA delegation in the six-party talks with North Korea during the George W. Bush administration.
Richardson, who served under former President Bill Clinton, lobbied Pyongyang on behalf of the Warmbier family for their son's release.
U.S citizen Otto Warmbier who was arrested while on a tourist visit to North Korea in January 2016 has died following his release from prison, The Washington Post reports.
"I kind of think the administration is there, but I think this will toughen them up", Keane said.
He was sentenced two months later to 15 years of hard labour for trying to steal an item bearing a propaganda slogan from his hotel in North Korea's capital, Pyongyang, the nation's state media said.
"Should there be a travel ban for USA citizens going there relative to this".
"Even today, there are many Korean nationals and American citizens who are detained in North Korea", Mr Moon added.
"It doesn't take much to get in trouble in North Korea".
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"I would have that first because if people are that stupid that they still want to go to that country then at least they assume the responsibility for their welfare", McCain said. "I believe we must now have the perception that North Korea is an irrational regime".
Warmbier had planned to study in China in his third year of college and heard about Chinese travel companies offering trips to North Korea.
Warmbier's death has only heightened U.S.
He noted that there are three other Americans detained in North Korea with "trumped-up charges against them".
Mr Trump tweeted: "While I greatly appreciate the efforts of President Xi & China to help with North Korea, it has not worked out".
"Our relations with North Korea have been absolutely terrible since 1950. So essentially, I think the United States has been doing largely the best it can with the North Korean problem and we just have to sort of hope for the best".
"There is nothing more tragic for a parent than to lose a child in the prime of life", a somber President Trump said Monday.
The US doesn't now prohibit its passports from being used to travel to any countries, even though financial restrictions limit US travel to Cuba and elsewhere.
South Korean President Moon Jae-in has been unable to pursue the engagement with the North he favors because of a string of North Korean missile tests.
The State Department says the dialogue will focus on ways to increase pressure on North Korea to give up its nuclear and missile programmes, but also cover such areas as counter-terrorism and territorial rivalries in the strategic South China Sea. The challenge will be, as you suggest, how to harmonize these approaches and also harmonize them with China's approach in the region, which certainly sees the need for a change in behavior in North Korea, but they're anxious about instability.
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