Biden said that Washington had offered Covid-19 vaccines to Pyongyang but "got no response".
US President Joe Biden has said that any potential meeting with North Korea's leader will depend on whether Kim Jong-un is "sincere".
Biden, who is in Seoul for his first trip to Asia as president, made the statement at a joint press conference with South Korean President Yoon Suk-yeol on Saturday.
The two leaders announced they would look at ramping up joint military exercises -- something that always infuriates North Korea, which views them as rehearsals for an invasion.
"We also discussed whether we'd need to come up with various types of joint drills in case of a nuclear attack," Yoon said.
Biden added that Washington had offered Covid-19 vaccines to Pyongyang but "got no response" despite a spiralling epidemic in North Korea, where nearly 2.5 million people have fallen sick with "fever".
READ MORE: Biden begins Asia tour with aim to cement economic, security ties
Threat of a nuclear test
Biden's predecessor Donald Trump met Kim for a round of high-profile diplomacy, but talks collapsed in 2019.
Kim has since doubled down on his programme of military modernisation.
Pyongyang has conducted a blitz of sanctions-busting weapons tests this year, including firing an intercontinental ballistic missile at full range.
Biden's Asia tour, aiming to shore up economic and security ties with regional allies, has been overshadowed by the threat of a North Korea weapons test.
The United States and South Korea have been warning for weeks that the North could carry out a nuclear test any day, and Washington said it could even come while Biden is in the region.
READ MORE: Biden could see North Korea's 'nuclear, missile tests' during Asia trip
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