Three Senate Democrats want Trump administration officials to keep a closer eye on the banks handing out aid to small businesses after some companies said they had received less than they expected, without explanation.

In a letter to Treasury Secretary Steven Mnuchin and Small Business Administrator Jovita Carranza on Wednesday, three members of the Senate Banking Committee asked for more oversight of banks making loans under the Paycheck Protection Program. The program is designed to provide forgivable loans that help small businesses pay their employees and some of their overhead during the coronavirus lockdowns.

But some business owners told The New York Times that they had not received as much money as they had asked for, and said they had been told that the decision was made by the banks — not the Small Business Administration, which is funding the program.

“Whether inadvertent or intentional, this troubling report warrants a response from your agencies,” the senators, Sherrod Brown of Ohio, Robert Menendez of New Jersey and Tina Smith of Minnesota, wrote in the letter.

The issue poses a significant problem for borrowers. Treasury rules say that for Paycheck Protection Program loans to be forgiven, businesses must spend the money in precise ways, including rehiring a certain portion of their employees. If the amount they receive isn’t enough to rehire enough employees, their loans cannot be forgiven.

The senators asked Mr. Mnuchin and Ms. Carranza to offer those borrowers options for getting additional funds to cover the gap. They also asked whether the officials had a plan for identifying which borrowers had not gotten as much money as they needed and determining the reason for the discrepancy.

It was not clear how many small businesses received less money than they asked for under the program, but borrowers seeking loans from Citizens Financial Group and Bank of America reported experiencing that problem.

At least seven borrowers posted about the issue on a page on Bank of America’s website that its customers can use as a discussion forum. The Times spoke with four additional borrowers experiencing the problem. A Bank of America representative advised users on the website to contact the bank for help, and a bank spokesman told The Times that the bank was working to correct any problems that borrowers reported.

The senators said small businesses needed all the help they could get while competing against larger, wealthier clients for banks’ attention. “Answers to these questions will help ensure that eligible small businesses are not further disadvantaged by lenders shorting them on P.P.P. loans,” they wrote.