Jennifer Kelly, a spokeswoman for the S.B.A. said in a statement that “this unprecedented global pandemic requires an unprecedented public-private response, and every hurdle that impedes, slows, or otherwise frustrates that response is being cleared in consultation with legal and ethics officials.”

The agency has turned to a range of companies to buttress its ability to process the disaster loans as well as the new $349 billion loan program for small businesses that opened on Friday.

On Sunday, the agency’s Office of Disaster Assistance issued an emergency $50 million contract to support its processing of coronavirus disaster loans to a Virginia-based government contractor called RER Solutions. It is partnering on its S.B.A. work with Rocket Loans, a Detroit-based company that provides consumer loans online.

Rocket Loans is part of a family of companies founded by the billionaire Dan Gilbert, who also co-founded Quicken Loans, which donated $750,000 to Mr. Trump’s inauguration and $67,000 to the committee that hosted the 2016 Republican convention. Mr. Gilbert has visited the White House, where Mr. Trump singled him out as “a great friend of mine, a supporter and great guy.”

Quicken Loans last year paid $32.5 million to settle a years-old lawsuit in which it was accused by the Justice Department of making hundreds of improper loans through the Federal Housing Administration’s lending program, costing the agency millions of dollars.

The S.B.A. contract with RER Solutions, which is for “data analysis and loan recommendation services for Covid-19,” appears to be related to a $10-million-per-year contract that RER signed with the S.B.A. in late 2018 for similar services related to processing disaster loan applications. Rocket Loans was a subcontractor on that work.

“We are stepping up to help solve problems under an existing contract,” said Aaron Emerson, a spokesman for Rocket Loans, adding “we were tapped to help the S.B.A. process applications.”