The one-page letter said that the “underlying source” of money for a series of personal loans Mr. Cruz made to his Senate campaign in Texas included both bank loans, which totaled as much as $1 million. Both loans were “inadvertently omitted” from the required filings, the letter said. Previously, Mr. Cruz had acknowledged only using the loan from Goldman for his campaign.

The latest disclosure casts further doubt on his oft-stated story of having liquidated his entire family savings of slightly more than $1 million to fuel a come-from-behind win in the Republican primary. The tale has become part of a campaign narrative of a populist, scrappy Mr. Cruz putting everything on the line to overcome a wealthy establishment opponent.

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.