The proceedings seriously complicate Joe Biden's re-election campaign as Republicans search for a distraction in the wake of Donald Trump's conviction last week of 34 felony counts of falsified business records.
In a show of support, Jill Biden, the first lady, was at the federal courthouse in Delaware where her stepson is facing trial.
In a statement, the president said that as a father he had "boundless love for my son, confidence in him, and respect for his strength".
Prosecutors allege Hunter Biden lied about his drug use on application forms when he bought a handgun in 2018, while in the throes of addiction.
In theory, he could face a jail sentence, but it is widely regarded as unlikely.
"I am the president, but I am also a dad," Biden said, adding that he would not comment further on the federal case.
Hunter Biden, the president's youngest and only surviving son, has struggled with drug addiction and a troubled private life.
"Jill and I love our son, and we are so proud of the man he is today," the president wrote. "Hunter's resilience in the face of adversity and the strength he has brought to his recovery are inspiring to us."
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