Her comments came ahead of a visit on Sunday by US Secretary of State Mike Pompeo to North Korea, where he will meet strongman Kim Jong Un in an effort to further the denuclearization effort.
Pompeo brushed aside suggestions of differences between himself and Trump over a timeline for North Korea to give up its nuclear weapons.
He will then fly to Japan and China to meet his counterparts there, according to the US State Department.
After the trip to Pyongyang, Pompeo will head to Seoul, where he will meet President Moon Jae-in, who has helped spearhead the reconciliation efforts with North Korea.
Pompeo's return to Pyongyang comes in line with his meeting with North Korean Foreign Minister Ri Yong-ho on the sidelines of the U.N. General Assembly last week.
"I think it shows forward progress and momentum that the secretary is making his fourth trip in less than a year", State Department Spokeswoman Heather Nauert told reporters. Pompeo expressed hope there would be major North Korean disarmament by the end of Trump's first term in January 2021, . but a week later.
An end to the Korean War in return for the verified dismantling of its major North Korean nuclear facility: South Korea's foreign minister on Wednesday proposed this tradeoff to unblock stalled negotiations between the United States and North Korea.
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He is expected to discuss a planned second summit between Kim and U.S. President Donald Trump following the previous one in Singapore, June 12.
-North Korea consensus on denuclearization is critical in meeting this commitment.
Analysts speculated the USA and North Korea may already have reached a consensus to some extent over denuclearization methods and a declaration ending the war.
Pompeo stressed that in the meantime worldwide sanctions would have to remain in place on North Korea.
"I don't think Pompeo's trip, Saturday, would have been possible unless the two countries had a coordinated agenda regarding denuclearization", said Cho Sung-ryul, a senior researcher at the Institute for National Security Strategy.
"We want it fast, but we're not going to play the time game", he said, adding that his reference last month to 2021 was repeating a comment made by the North and South Korean leaders at a summit last month in Pyongyang.
"On the negotiating table will be North Korea's plan to dismantle the Yongbyon facilities allowing outside inspectors, and the US' agreement to declare an end to the Korean War and partial sanctions relief", he said. "We fell in love", he said. "I think the two sides adjusted their differences on what initial steps North Korea and the U.S. will each take", said Koh Yu-hwan, a Dongguk University professor.