Senate Minority Leader Chuck Schumer, a Democrat from New York, speaks during a news conference on Capitol Hill in Washington, D.C., on Tuesday, April 21, 2020.

Three leading Democratic senators are urging the Small Business Administration to investigate whether banks gave the wealthy preferential treatment as they doled out money from a key aid program.

In a letter dated Thursday, Democratic Senate Minority Leader Chuck Schumer and Sens. Ben Cardin of Maryland and Sherrod Brown of Ohio asked the agency's inspector general to look into reports that lenders have "prioritized the applications of their larger and wealthier clients to the detriment of smaller business" damaged by the coronavirus pandemic.

The lawmakers also asked the SBA to "provide recommendations" by May 8 on the measures it is taking to "ensure small businesses get the money they need and are treated fairly" by lenders participating in the program.

The senators announced their letter on the day President Donald Trump signed a bill into law to replenish the Paycheck Protection Program, which gives small companies forgivable loans if they use the money on expenses such as payroll and rent. The initial $350 billion funding pool created last month evaporated quickly, and the new law puts another $310 billion into the program — including $60 billion specifically for small lenders.

Some lawmakers have put pressure on the SBA to tweak the program after a chaotic rollout, which included some larger companies getting aid while thousands of smaller applicants were left in limbo. The agency issued guidance Thursday that aims to make it harder for public companies to access the aid.

The letter, announced Friday, adds to the pressure the Trump administration faces from lawmakers as it oversees an unprecedented flood of emergency spending that now tops $2.5 trillion. Schumer is the leading Senate Democrat, while Cardin and Brown are the ranking members of the Small Business and Banking committees, respectively.

An SBA spokesperson did not immediately respond to CNBC's request to comment on whether the agency would investigate the reports or further change its rules for the program.

The senators pointed to a New York Times report saying some of the largest American banks such as JPMorgan Chase and Citibank processed loans from private and commercial banking customers before moving on to applications from small businesses. The newspaper reported that private bank clients at Citi simply had to submit paperwork to their bankers, who filed applications for them.

"Nearly all" of the 8,500 private and commercial applicants at Chase got a loan, versus only 18,000 of the more than 300,000 small business clients who tried to get aid, according to the Times. In a statement to CNBC this week, Chase said it "worked as quickly as possible in a race against time, volume, and manual processes." The company said the vast majority of its loans went to "smaller business clients."

Meanwhile, a Citi spokesperson told CNBC that five of the company's 6,573 loans went to private banking clients. Another 470 loans went to commercial banking clients.

A Citi spokesperson said "we strongly disagree" with the Times report and added that "there was no preferential treatment."

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