The Small Business Administration said Friday that hedge funds and private equity firms are ineligible for the small business relief program.

The move comes after reports that hedge funds had applied for the first round of the Paycheck Protection Program. That fed into a public backlash after the program's initial $350 billion was quickly exhausted and it was revealed that big public companies, rich universities and large restaurant chains had tapped the PPP.

"Hedge funds and private equity firms are primarily engaged in investment or speculation, and such businesses are therefore ineligible to receive a PPP loan," the SBA said in an update posted online. "The Administrator, in consultation with the Secretary, does not believe that Congress intended for these types of businesses, which are generally ineligible for section 7(a) loans under existing SBA regulations, to obtain PPP financing."

Lenders rely on the SBA guidance called an "interim final rule" to administer the massive effort, part of the Trump administration's $2 trillion-plus response to the coronavirus pandemic. The update comes after the SBA said Thursday that companies must certify they cannot tap other sources of funding, making it less likely that big publicly traded companies could use the facility.

It also encouraged public companies that have already used the PPP to return the funds within two weeks. Late Thursday, Ruth's Hospitality Group, owner of the Ruth's Chris Steak House chain, said it returned $20 million it got from the program, following a similar move from Shake Shack.

A senior administration official told CNBC that when loans are returned early, new loans can't be made against those funds until the latest round of PPP has been approved.

The rules posted Friday also state that if a business is currently in bankruptcy, it will not be approved for a loan. It also addressed questions about hospitals, gambling businesses and companies owned by private equity firms.

The update didn't prohibit PE-owned firms from applying for relief, but it stated that applicants must certify that "current economic uncertainty makes this loan request necessary."