Bank of America Corp. became the first giant bank to start accepting applications under a key federal program to support small businesses, saying it had received about 10,000 applications by 10 a.m. ET on the day of the program's launch.

Chairman, President and CEO Brian Moynihan said employees worked all night to add a new component to the company's core banking app in time for the launch of the Paycheck Protection Program on April 3. In an interview on CNBC, he said branches were open for small-business customers to apply, but that the process could be done entirely digitally.

BofA is accepting applications from existing small-business customers, starting with those that already have loans with the bank. Moynihan encouraged potential borrowers to go to banks where they already have relationships, in line with guidance from Treasury Secretary Steven Mnuchin.

"We want everyone to go back to their borrowing bank to get the application because that will be easier to process," and faster, Moynihan said.

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BofA still has more to do to complete the enhancement to its app. "We're trying to make sure it's all fully operational behind the scenes," Moynihan said. "That takes a little more work."

Mnuchin said on March 31 that the government expects applications to be approved the same day they are submitted. Moynihan said, "You'll see the money start to go out the door once these applications are processed over the next short period of time."

Moynihan said there was a conference call among banks across the country on the morning of April 3, and that others are also setting up to accept applications. The Paycheck Protection Program was established by the $2 trillion coronavirus relief package enacted on March 27 and provides $350 billion in low-cost loans to small businesses forced to shut down or otherwise hurt by the pandemic. Most of the loans, which are targeted toward covering payroll expenses, rent, mortgage interest and utilities, will convert into grants. The loans are being made by banks and are backed by the Small Business Administration.

The scramble to launch the program has been marked by confusion, pushback from banks concerned that they will be liable for underwriting errors and objecting to other elements of the program. Most top SBA lenders did not begin accepting applications on the morning of April 3.

Moynihan said payments activity across BofA's network had fallen from about $60 billion a week to about $40 billion a week because of the pandemic. He guessed it would be "a while" before the lost activity resumes.

"We don't know where we'll be yet and we'll keep you posted over the next few weeks," he said. "But to get the rest of that $20 billion a week of payments restarted you'll have to see activities opening up again, and that means winning the war on the virus."