North Korea has also canceled high-level talks with South Korea that were scheduled for Wednesday local time over those same drills.
"If the U.S. and the South Korean government thinks that the improvement of North-South relationship and the U.S. talk made possible by our leading and generous efforts and actions as a pardon to open play-with-fire fuss like this war drill anytime, there is no greater misjudgment than that," North Korean state media agency KCNA said in a dispatch.
"We have no choice but to stop the North-South high-level talk scheduled for the 16th under the ugly circumstances where there is indiscreet North-invading war fuss and fight rampage," KCNA said. "... The U.S. must contemplate on the fate of the scheduled Korea-U.S. head meeting with the provocative military situation created with the South Korean government.
"We will keep sharp eyes on the U.S. and the South Korean government's future attitude."
The summit between the American and North Korean leader was first announced in March and Trump tweeted the scheduled date -- June 12 -- and location -- Singapore -- last week.
Three Americans that were held in North Korea for more than a year each were released last week, in what was seen by many as a gesture of goodwill before the scheduled summit.
The U.S. has not heard from North Korea and is still planning for the summit to go ahead, State Department spokesperson Heather Nauert said.
"What we have to go on is what Kim Jong Un has said before, that he understands and appreciates the importance to the United States of having these joint exercises, the Republic of Korea has as well," Nauert said. "We've received no formal or even informal notification of anything."
As the U.S. has done on multiple previous occasions, Nauert defended the exercises as "legal," "planned well, well in advance" and "not provocative."
Col. Rob Manning, a Department of Defense spokesperson, said in a statement the exercises are "part of the ROK-U.S. Alliances’ routine, annual training program to maintain a foundation of military readiness."
"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 said.
Separately, a senior State Department official told reporters the U.S. and South Korea were in touch "a short while ago," but referred questions on that to South Korea. That official confirmed that there's been no contact from North Korea.
In a statement, the White House said: “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.”
ABC News' Nataly Pak, Luis Martinez and Meghan Keneally contributed to this report.