However, Ryder said the Pentagon "must be prepared to adjust as appropriate" if negotiations with North Korea advance, indicating that there could be changes to the military exercises with South Korea that are scheduled to take place next year.
U.S. President Donald Trump speaks during a news conference following Tuesday's midterm U.S. congressional elections at the White House in Washington, U.S., November 7, 2018.
"We will reconvene when our respective schedules permit", she added in a statement.
The State Department said early on Wednesday that the meeting had been postponed, but gave no reason, raising concerns that talks aimed at persuading North Korea to give up its nuclear arms could break down.
Talks between President Donald Trump's top diplomat and the North Korean delegation, which had been due on Thursday, "will now take place at a later date", State Department spokeswoman Heather Nauert said.
United States Secretary of State Michael Pompeo on Tuesday abruptly postponed a meeting with a top North Korean official in NY scheduled for Thursday, in a setback to peace talks between the two countries, AFP reported.
"Before trust is built up between the USA and North Korea, demanding that we give the USA a list of our fissile materials, nuclear weapons and delivery systems is the same as telling us to submit a list of targets for attacks", he quoted Kim as saying.More news: Dani Carvajal backs sacked Julen Lopetegui as best coach he's ever had
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The cancellation comes amid North Korean threats to restart its nuclear development unless the US begins to remove sanctions - a step the administration says it will not take until North Korea meaningfully moves to denuclearize, which it so far has not done.
His insistence on being in "no rush" - which he repeated five times in different formulations - may be a response to criticism that North Korea has not moved quickly enough since the summit. "We're in no rush".
"And nobody else could have done what I have done", he said.
State-run media, in a statement last week, warned that North Korea was "seriously" considering a return to a guiding policy of building nuclear weapons and said that sanctions were "incompatible" with improving relations with Washington.
South Korea, which has worked to encourage U.S.
After the cancellation, South Korea tried to quell concerns Wednesday, with presidential spokesperson Kim Eui-kyeom telling reporters, "We don't believe that the delay means the North Korea-U.S. summit won't happen or momentum for the summit has been lost", according to Reuters. Instead of following through on that, in recent days North Korea has been criticizing the US over its sanctions, threatening last Friday to bring back its "byongjin" policy - advancing its nuclear arsenal and economic development at the same time.
But Pompeo abruptly postponed the talks in NY.
Democrats have said they are determined to obtain more information about meetings between Trump and Pompeo and Kim, anxious that Trump is so eager to make a "great deal" that he will give Kim too much with little in return.