SEOUL, South Korea — North Korea launched at least two unidentified projectiles toward the sea on Tuesday, South Korea’s military said, hours after the North offered to resume nuclear diplomacy with the United States but warned its dealings with Washington may end without new U.S. proposals.

The North’s projectile launches and demand for new proposals 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 United States to provide it with security guarantees and extensive relief from U.S.-led sanctions in return for limited denuclearization steps.

The North Korean projectiles fired from its South Phyongan province, which surrounds its capital city of Pyongyang, flew across the country and in the direction of the waters off its east coast, according to South Korea’s Joint Chiefs of Staff and Defense Ministry.

The military said South Korea will monitor possible additional launches by North Korea but gave no further details, including exactly what projectile North Korea fired.

Tuesday’s launches were the eighth such launches since late July and the first since Aug. 24. The previous seven launches have revealed short-range missile and rocket artillery systems that experts say would potentially expand its capabilities to strike targets throughout South Korea, including U.S. military bases there.

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.

President Donald Trump called North Korea’s announcement “interesting.”

“We’ll see what happens,” Trump said. “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.

South Korea’s presidential office said national security adviser Chung Eui-yong presided over an emergency National Security Council meeting where officials expressed “strong concern” over the continuing short-range launches by the North.

In the late-night statement carried by state media, Choe said North Korea is willing to sit down with the United States “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 United States 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.

She warned that “if the U.S. side fingers again the worn-out scenario which has nothing to do with new decision methods at the DPRK-U.S. working negotiation to be held with so much effort, the DPRK-U.S. dealings may come to an end.”

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