The Small Business Administration’s third round of Paycheck Protection Program coronavirus relief lending has steadily grown to top 400,000 loans worth about $35 billion in its first two weeks as a persistent economic crisis means small businesses are still seeking help.

The government’s new phased approach to distributing the $284 billion in recently allocated PPP funds means it’s unlikely that the money will run out as it did in April. This time, the SBA gave a head start to smaller banks and those likely to serve low-income and minority communities. And it added a new set of automated compliance checks to prevent fraud and abuse of public funds, something that has created new safeguards but also led more applications to be rejected.

Acting SBA administrator Tami Perriello said the agency wants to move faster while also carrying out necessary checks.

“The agency is committed to making sure compliance checks are executed on the front-end,” Perriello said in a statement.

She added that the SBA “is also committed to addressing issues more efficiently moving forward, to ensure fair and equitable access to small businesses in every community.”

The PPP is a massive coronavirus relief program created last year under the Cares Act. It offers loans to small businesses at ultralow interest rates and gives recipients the opportunity to have the loan forgiven.

Despite a chaotic, confusing rollout in April, the loan program quickly scaled up to serve millions of small businesses and contributed to a surprise drop in unemployment in the early months of the crisis.

It also drew controversy when a lack of guardrails allowed an array of larger and otherwise wealthy organizations to receive the taxpayer-subsidized funds. More than 1,000 Sonic locations received PPP loans, raising questions about whether large restaurant chains were raiding a fund meant for mom-and-pop shops.

Some publicly traded companies received PPP loans and were asked to return the money. Some did; others kept the funding and later sent money back to Wall Street.

When implementing the third round of funding, Congress put new limits on who could receive PPP loans, even as it approved hundreds of billions of dollars of new funding for the program.

The first week of loan funding starting Jan. 11 was open only to “Community Financial Institutions,” which are typically better at lending to businesses in low-income areas. It was not until Jan. 19 that larger banks were allowed to participate.

The rollout has not been without hiccups. In a letter Monday, the American Bankers Association pointed out several apparent glitches that the organization said “are preventing the program from fully supporting small businesses in need.”

Aside from problems with loan applications and confusion over how to document certain aspects of the application process, ABA President Rob Nichols wrote, lenders are receiving “a high number of incorrect error messages” when they attempt to apply for PPP loans on their clients’ behalf.

The SBA, for its part, said “anomalies” were identified in just under 5 percent of loan applications, indicating that those loans will require additional follow-up.

Lenders note that although there are some new obstacles with the third round of PPP funding, the SBA is steadily improving its processes. It phased out a much-maligned system called E-Tran that repeatedly crashed last year, one lender said.

Sam Sidhu, vice chairman and chief operating officer at Pennsylvania-based Customers Bank, said his bank received well over 50,000 applications for the third round of PPP funding. The beefed-up approval process meant that his bank could not start funding loans until Friday after the official launch Tuesday.

At one point last week, Sidhu said, the SBA was rejecting about 30 percent of its applicants. Some applicants are being filtered out by “do not fund” lists that were put in place to spot fraud. But others appeared to be improperly rejected based on technical aspects of how a loan application is submitted.

Still, Sidhu noted that the program has evolved markedly since April. That is partially because the economic crisis has evolved, too.

“In April and May, you had more targeted areas that were impacted” by the economic crisis, Sidhu said. “What’s happened over the last four months is there are a lot more areas that are impacted in a material way from covid. We’re seeing majority new customers come to us.”