The warning comes as KCNA reported North Korea has suspended talks with South Korea because of a joint military drill conducted by South Korea and the US.
"We are aware of the South Korean media report. The United States will look at what North Korea has said independently, and continue to coordinate closely with our allies," White House press secretary Sarah Sanders said in a statement.
However, the White House was caught off guard by the reports, according to aides. One official affirmed an assertion from the State Department that it has received no information from Pyongyang about the status of the talks.
State Department spokeswoman Heather Nauert defended joint US-South Korean military exercises Tuesday and said the US had not heard of any disruptions to either the planned exercises or the upcoming summit.
While media reports were just emerging as she took the briefing room podium, Nauert said, "We have not heard anything from that government or the government of South Korea to indicate that we would not continue conducting these exercises or that we would not continue planning for our meeting between President Trump and Kim Jong Un next month."
"Let's not get ahead of ourselves," she cautioned to reporters. "This news just came out. We need to verify it to get additional information on that but we're going forward in planning our meetings next month."
Meetings are underway now between White House officials, the National Security Council and Defense Department, the official said.
"North Korea's actions today are not surprising. They come straight from the Kim Jong Il playbook on negotiations: Raise expectations of a diplomatic breakthrough, cancel/suggest Pyongyang might cancel the meeting and then push for more concessions to have the meeting," according to Anthony Ruggiero, senior fellow at the Foundation for Defense of Democracies.
"The Trump administration must see through this blatant attempt to coerce additional concessions. The US should continue the defensive military exercises and remind Kim that the maximum pressure campaign will be increased if North Korea pulls out of the summit," he added.
Talks between the Koreas were set to resume Wednesday. South Korea's Unification Ministry said it received a written notice ahead of the postponement announcement on Wednesday from top North Korean negotiator Ri Son Gwon, according to an official with the Unification Ministry.
In a statement, the ministry said it was "regrettable that the North unilaterally postponed the talks due to the annual [South Korea-US] joint air combat drills."
"Such action by the North is inconsistent with the fundamental spirit and purpose of the Panmunjeom Declaration agreed by the South and North leaders on April 27," it added.
The KCNA report said the Max Thunder 2018 air combat drill was against the Panmunjom declaration -- signed last month between the Koreas -- wherein they agreed to cease all hostile acts against each other.
KCNA labeled the Max Thunder drills a "deliberate provocation."
The Pentagon said Tuesday that "Republic of Korea (ROK) and US military forces are currently engaged in the recurring, annual ROK-U.S. spring exercises, to include exercises Foal Eagle 2018 and Max Thunder 2018."
The exercise involves the US Air Force and South Korean forces with about 2,000 troops participating, a Department of Defense official told CNN.
"These defensive exercises are part of the ROK-U.S. Alliance's routine, annual training program to maintain a foundation of military readiness," a statement from Pentagon spokesman Col. Rob Manning noted.
"The purpose of the training is to enhance the ROK-U.S. Alliance's ability to defend the ROK and enhance interoperability and readiness. While we will not discuss specifics, the defensive nature of these combined exercises has been clear for many decades and has not changed," Manning added.
In the Unification Ministry statement, Seoul pledged to continue pursuing "necessary measures through close consultations with relevant ministries to achieve sustainable development of inter-Korean relations and a permanent peace settlement through the implementation of the Panmunjeom Declaration."
CNN's Kevin Liptak, Ryan Browne, Barbara Starr, Laura Koran and Jeff Zeleny contributed to this report