Charities have to register in states where they raise money so that officials there are aware of their activities. The charities may also have to make financial filings with the state in which they register. The process helps make charities more accountable to donors at the state level.

“The Donald J. Trump Foundation is aware of the state charitable-solicitation requirements and believes it was in compliance,” the foundation said in a statement sent by Hope Hicks, a spokeswoman for Mr. Trump. Iowa does not require charities to register before soliciting, the statement noted. It also said the fund-raising included “a one-time online donation option for the event, which does not require advance registration.”

Charity law specialists said they were not aware of any such sweeping exemption. Mr. Trump’s foundation declined to comment further when asked to explain why it did not need to register in states beyond Iowa for the online fund-raiser.

The foundation also may not have registered because it does not have a history of raising money through national appeals. In its statement, the foundation said it “has no plans to solicit funds in the future.”

Registration with the states need not be particularly burdensome. Charities can have state registrations handled for a fee by organizations that will do the paperwork. “Typically, charities, if they are of a decent size, will hire an outside firm to manage it for them,” Ms. Miniutti said.

While Mr. Trump’s foundation is unlikely to face stiff penalties for not registering, charity specialists noted that some states, like California and Pennsylvania, were stricter than others in enforcement. Officials from Pennsylvania and California confirmed that the Trump Foundation had not registered in those states.

“No charitable organization shall solicit contributions or have contributions solicited in its behalf before approval of its registration statement,” Pennsylvania’s charities law states.