President Xi Jinping delivered the message on Friday, state television said.
It comes as the White House Covid coordinator Dr Ashish Jha told CNN the 79-year-old is “doing just fine” and continues to have mild symptoms.
It remains unclear where the president contracted the virus from but contract tracing is ongoing.
Mr Biden recorded a video from the White House balcony telling people: “I’m doing well, getting a lot of work done. And, in the meantime, thanks for your concern. And keep the faith. It’s going to be OK.”
“Keeping busy!” he also tweeted.
Mr Biden’s first-day symptoms were mild because he is fully vaccinated and boosted, according to a statement issued by his physician, Dr Kevin O’Connor.
The president also is taking Paxlovid, an antiviral drug designed to reduce the severity of the disease.
Dr Jha said Mr Biden’s case was being prioritised, meaning it will likely take less than a week for sequencing to determine which variant of the virus Biden contracted.
Omicron’s highly contagious BA.5 sub-strain now makes up more than 65 per cent of US cases.
On Friday, Mr Biden was scheduled to meet virtually with his economic team and senior advisors to discuss congressional priorities.
At 79, he is the oldest person ever to be US president.
Asked about the possibility Mr Biden might need to be hospitalised by local media, Dr Jha stressed that the president was “doing well” and added that there were “obviously a lot of resources available here at the White House to take care of him.”
“Walter Reed is always on standby for presidents. That’s always an option,” he added. “That’s true whether the president had Covid or not.”
Mr Biden plans to continue to isolate until he tests negative, the White House said.