He said he saw no need for a new lockdown “for now… if people are vaccinated and wear their masks”.
Cases have been found in Canada, and the US has imposed travel bans on eight southern African countries.
Mr Biden added that pharmaceutical companies were making contingency plans for new jabs if they are needed.
At the White House on Monday, the president said it was “almost inevitable” that Omicron, first reported by South Africa, would be found in the US eventually.
“We’re going to fight and beat this new variant,” he said.
Late last week, the US announced restrictions on travellers from South Africa, Botswana, Zimbabwe, Namibia, Lesotho, Eswatini, Mozambique and Malawi. Canada, the UK and the EU and other countries have also restricted travel from southern Africa.
On Sunday, Canada said the Omicron variant had been discovered in two patients who had recently travelled to Nigeria. A third case was announced on Monday.
Mr Biden said the travel ban had bought some time for the US to study the new variant. While the World Health Organization (WHO) has deemed Omicron a “variant of concern”, it is still not clear whether it is associated with more transmission or more risk of evading vaccines.
Critics noted that Mr Biden accused former President Donald Trump of “hysterical xenophobia” after he limited travel from China in January 2020 as the coronavirus spread in the US.
Republican Florida Governor Ron DeSantis dismissed the latest flight restrictions as a “knee-jerk reaction”. The state has taken steps to ban Covid-19 vaccine and mask mandates in recent months.
“In Florida, we will not let them lock you down,” Mr DeSantis said. “We will not let them take your job. We will not let them harm your businesses. We will not let them close your schools.”
While Mr Biden once again urged Americans on Monday to wear masks, he has come under fire for flouting his own rules.
He was pictured without a mask covering his face over the Thanksgiving weekend where he stayed in Nantucket, Massachusetts – at one point inside a shop that had a sign on the window requiring customers to wear face coverings.
First Lady Jill Biden was also criticised on Monday as she appeared in the White House without a mask, reading to a group of schoolchildren who were all masked and socially distanced.