The North has insisted that Washington offer it new concessions by the end of 2019.
The pair have met three times since June 2018 but with little progress towards denuclearization.
The president was responding to a conservative commentator's tweet about a particularly visceral attack on Biden issued Friday by North Korea.
It was not immediately clear what had provoked Pyongyang's ire, but Biden's campaign released an ad this week condemning Trump's foreign policy.
Kim criticised the appearance of the buildings constructed by Southern companies.
It is not the first time the North has followed up an offer of talks with a weapons test.
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The country held a blockchain and cyptocurrency conference in April this year.
The alleged birthplace of former North Korean leader Kim Jong Il has become a pilgrimage destination.
The test announced Thursday was the first public weapons test by North Korea since President Donald Trump's historic meeting with Kim Jong Un in Singapore last year.
Days after the Hanoi summit between U.S. President Donald Trump and North Korean leader Kim Jong Un, reports say North Korea has started rebuilding a part of its missile launch site.
North Korea is set to hold the national conference of primary information workers of the party, for the first time in 18 years, right after the Trump-Kim summit in Hanoi, Vietnam.
In a meeting with officials from the Senate Arms Committee, U.S. Forces Korea Commander Robert Abrams warned that North Korea's military program "remains unchecked."
U.S. President Donald Trump tries for the second time to seal a denuclearization deal with Kim Jong-un after failing the first time around.
The head of IAEA said there has been activity observed at Yongbyon, but "without access the agency cannot confirm the nature and purpose of these activities."
South Korea move to lift sanctions is aimed at encouraging North Korea down the path of denuclearization.
The "new line" of putting economic development first has been Kim's top priority this year.
Developed nations also bear responsibility because they import $350 billion worth of goods that are produced under suspicious circumstances.
Kim is expected to discuss with Chinese leaders his next steps after his nuclear summit with President Donald Trump last week.
We should not be surprised if one or both parties back-pedals from the joint statement at some stage.
Critics said the welcome Trump was giving Kim in Singapore would legitimize one of the world's worst human rights offenders.
The leaders promised in the document to "build a lasting and stable peace regime" on the Korean Peninsula