Within hours of the announcement, North Korea fired two unidentified projectiles from its South Pyongan province, South Korea's Joint Chiefs of Staff said, Presstv Reported.
The launches followed repeated short-range missile tests by North Korea since its leader Kim Jong-un agreed in a June 30 meeting with US President Donald Trump to reopen working-level talks stalled since their failed February summit in Hanoi. The talks have yet to resume despite repeated US appeals.
A senior Trump administration official said later: "We are aware of reports of projectiles launched from North Korea. We are continuing to monitor the situation and consulting closely with our allies in the region."
North Korean Vice Foreign Minister Choe Son Hui said in a statement carried by the North's official KCNA news agency Pyongyang was willing to have comprehensive discussions with the United States in late September "of the issues we have so far taken up" at a time and place agreed between both sides.
Trump was asked about the offer while speaking to reporters at the White House and called it "interesting". He also mentioned, as he often does, his "good relationship" with Kim.
"I just saw it as I'm coming out here, that they would like to meet. We'll see what happens," Trump said. "I always say having meetings is a good thing, not a bad thing."
Asked for comment on the North Korea statement, a US State Department spokeswoman said: "We don't have any meetings to announce at this time."
US Secretary of State Mike Pompeo said on Sunday he hoped for a return to denuclearization talks in the coming days or weeks, while reiterating the US objective of North Korea's complete denuclearization and saying Washington was disappointed by North Korean short-range missile tests.
Trump has sought to play down such short-range tests, saying they do not violate a North Korean freeze in nuclear and long-range missile tests in place since 2017. He emphasized this freeze again when he spoke on Monday, before the latest launches.