"I think we're going to win in Virginia. I think... it’s going to be a tight race," Biden said on Tuesday during his press briefing at the UN Climate Change Conference in Glasgow.
The president said he expected the final results to be announced after midnight and the outcome will depend on the voters' turnout.
"I think we're gonna win New Jersey as well," Biden added, referring to the governor elections in the state where Democratic incumbent Phil Murphy is leading in the race against Republican nominee Jack Ciatarelli.
Virginia's and New Jersey's elections are seen as representative of national political trends as they are held a year after Biden beat former President Donald Trump.
After the Delta surge, the US abrupt withdrawal from Afghanistan in August and disagreements among Congress Democratic members on Biden's infrastructure bill, the president's approval rating has fallen down to 42 percent.
The figure is lower than any other modern first-year president's rating at a similar point in time - except for Trump, according to the most recent national NBC News poll.
Besides the idea that its results might be interpreted as an early test of Biden, the race is also believed to have the ability to set the tone for 2022 US midterm elections and the 2024 presidential race, which is anticipated to see Trump running for office again.
In 2017, Democrats won the governorships in both Virginia and New Jersey following the election of Trump a year before the race.