The administrator of a key U.S. small business lending program to support companies devastated by coronavirus shutdowns said Thursday it has run out of funds due to massive demand.

The Small Business Administration, which was tasked with managing the $349 billion program, said on its website it was unable to accept new applications "based on available appropriations funding."

The statement comes as lawmakers in Congress argue over the next round of stimulus measures following an unprecedented series of emergency initiatives to prop up the U.S. economy.

The Paycheck Protection Program (PPP) provides loans to businesses with fewer than 500 employees to cover eight weeks of payroll or rent.

The loans convert to grants if restaurants, shops and other businesses maintain their employees or rehire laid-off workers by June 30.

The scale of the program, launched less than two weeks ago, has proved challenging to the SBA, a normally sleepy government agency whose lending operation is typically a fraction of the PPP's size.

Some prominent lenders, including JPMorgan Chase and Wells Fargo, said Thursday they would continue to process paperwork from small businesses in anticipation of additional funding from Washington.

"We know Congress is currently considering another round of funds soon," said a statement from Jennifer Roberts, head of Chase Business Banking at JPMorgan.

"In the interim, we will continue to work our existing queue of applications so we can be ready."