More than 25,000 troops were deployed to Washington DC for his inauguration after violence earlier this month.
Images spread on Thursday showing them forced to rest in a nearby parking garage after lawmakers returned.
The conditions sparked anger among politicians, and some state governors recalled troops over the controversy.
Mr Biden called the chief of the National Guard Bureau on Friday to apologise and ask what could be done, according to US media reports.
First Lady Jill Biden also visited some of the troops to thank them personally, bringing biscuits from the White House as a gift.