North Korea launched two unidentified projectiles into the sea Tuesday, South Korea's military said, hours after the North offered to resume nuclear diplomacy with the United States later this month. South Korea's Joint Chiefs of Staff said in a statement that the North Korean projectiles fired from its South Phyongan province, which surrounds its capital city of Pyongyang, flew across the country before landing in the waters off its east coast.

It said South Korea will monitor possible additional launches by North Korea. But the statement gave no further details like exactly what projectile North Korea fired.

A senior Trump administration official told CBS News the White House was aware of the launch and is monitoring the situation.

Get Breaking News Delivered to Your Inbox

On Monday night, the North's first vice foreign minister, Choe Son Hui, said North Korea is willing to resume nuclear diplomacy with the United States in late September but that Washington must come to the negotiating table with acceptable new proposals. She said if the proposals don't satisfy North Korea, dealings between the two countries may come to an end.

Choe's statement and the following projectile launches were apparently aimed at pressuring the United States to make concessions when the North Korea-U.S. talks restart. North Korea is widely believed to want the U.S. to provide it with security guarantees and extensive relief from U.S.-led sanctions in return for limited denuclearization steps.

President Trump called North Korea's announcement "interesting."

"We'll see what happens," the president told reporters earlier Monday. "In the meantime, we have our hostages back, we're getting the remains of our great heroes back and we've had no nuclear testing for a long time."

There was no immediate comment from the White House following reports of the launches.

In the late-night statement carried by state media, Choe said North Korea is willing to sit down with the U.S. "for comprehensive discussions in late September of the issues we have so far taken up, at a time and place to be agreed."

Choe said she hopes the U.S. will bring "a proposal geared to the interests of the DPRK and the U.S. and based on decision methods acceptable to us." DPRK stands for the Democratic People's Republic of Korea, the North's official name.

Kim and Mr. Trump last met at the Korean border in late June and agreed to restart diplomacy, but there have no public meetings between the sides since then.