Donald Trump’s presidential campaign provided new details about the tax he paid after his charitable foundation made an improper donation to a political group, though experts in nonprofit law say he may still owe an additional tax.

Mr. Trump and his campaign have been responding to increasing scrutiny of the gift to a group connected to Florida Attorney General Pam Bondi, which was given in 2013 just as Trump University was facing potential legal scrutiny by her office.

It is “obvious” that paying the donation from the foundation, as opposed to Mr. Trump’s checkbook, was an inadvertent mistake, campaign spokeswoman Hope Hicks said Wednesday. Charities, which receive tax-deductible donations, are prohibited from giving money to political groups.

“The press seems to ignore the fact that there was not, and could not be, any intent or motive for the foundation to make the payment rather than Mr. Trump,” Ms. Hicks wrote in an email. “All political contributions are publicly reported and a matter of public record, as are all foundation expenditures.”

The attention drawn to the Donald J. Trump Foundation’s improper transaction coincides with a new push by his campaign to tarnish Democratic rival Hillary Clinton because of her ties to her family foundation.