Before U.S. President Joe Biden left South Korea for Japan Sunday, he left a brief message for Kim Jong Un, whose nuclear sabre-rattling has risked overshadowing the U.S. leader's first Asia trip: "Hello. Period."

He offered the succinct greeting when reporters asked whether he had anything to say to North Korea's leader, highlighting his administration's openness to dialogue with Pyongyang, even as they look to ramp up joint military exercises with South Korea.

Biden said that he was "not concerned" about the risks of a fresh weapons test while he was in the region – something U.S. officials have warned of repeatedly – saying: "We are prepared for anything North Korea does."

He has spent two days with South Korea's newly elected President Yoon Suk-yeol, with the pair saying Saturday that "considering the evolving threat" from Pyongyang, they were looking at expanding the "scope and scale" of joint military exercises.

North Korea has conducted a blitz of sanctions-busting weapons tests this year, including firing an intercontinental ballistic missile at the full range for the first time since 2017, with satellite imagery indicating a nuclear test is looming.

Joint exercises had been scaled back due to COVID-19 and in order for Biden and Yoon's predecessors, Donald Trump and Moon Jae-in, to embark on a round of high-profile but ultimately unsuccessful diplomacy with North Korea.

In contrast to the dovish Moon, Yoon said he and Biden discussed possible "joint drills to prepare for a nuclear attack" and called for more tactical U.S. assets to be deployed to the region.

Any buildup of forces or expansion of joint military exercises would likely enrage Pyongyang, which views the drills as rehearsals for invasion.

North Korea's weapons testing schedule may also be affected by a raging COVID-19 outbreak.

More than 2.6 million cases of "fever" have been reported since the omicron coronavirus variant was first detected in April, state media said Sunday.

Biden and Yoon extended an offer of help to North Korea, which has an unvaccinated population and a crumbling health care system, saying in a statement they were "willing to work with the international community to provide assistance."

Biden added that he would not exclude a meeting with Kim if the North Korean leader were "sincere."

"We've offered vaccines, not only to North Korea but to China as well and we're prepared to do that immediately," Biden said at a press conference with Yoon. "We've got no response."