His letter to the Federal Election Commission came after The New York Times reported that at least some of the “personal funds” Mr. Cruz and his wife, Heidi, put into his campaign actually came from a large loan from Goldman Sachs, where Mrs. Cruz works. The loan, for up to $500,000, was secured by holdings in a brokerage account at Goldman Sachs. The Cruz campaign called the failure to disclose the loan an honest mistake and said it would contact the election commission for guidance on how to amend its filings.

The Citibank loan, also for as much as $500,000, was a line of credit, and it is not clear from Mr. Cruz’s letter what collateral, if any, was used to obtain it. Mr. Cruz’s presidential campaign has declined to answer questions from The Times about the Citibank loan.

Kent Cooper, a former election commission official, said the letter from the Cruz campaign was still “lacking critical information” that candidates must report, including the exact amount of the loans and whether there were any co-signers. Federal law required that those details, and more, were to be reported during the primary and general election campaigns.

“This failure to disclose to the public,” Mr. Cooper said, “meant voters in Texas did not have the required information.”