The Federal Reserve said Monday that it plans to purchase short-term debt from a wider array of cash-strapped cities and counties, responding to concerns that some large U.S. municipalities including Baltimore and Detroit might have struggled to take advantage of its new $500 billion fund.

Now, cities with a population of 250,000 and counties with at least 500,000 residents may sell their municipal bonds directly to the central banking system, according to the Fed, which initially had set the bar so high that only 10 cities and 15 counties would have been eligible to sell their debt directly.

Under the new threshold, more than 80 cities and 120 counties now qualify, amounting to a major expansion of a $500 billion facility that state and local leaders see as critical as they brace for multibillion-dollar budget shortfalls in the wake of the coronavirus pandemic. It could help push down interest rates, ease borrowing and help local governments raise revenue, perhaps sparing them from debilitating cuts to local programs or their own workforces.

Many mayors and governors initially celebrated the effort, given that the Fed typically steers clear of the roughly $4 trillion municipal bond market, seeking to avoid the perception it is picking winners and losers. But some began to sour on it after reading the fine print, which opened direct bond sales to all states — but only to cities with a population of 1 million and counties with more than 2 million residents. Smaller municipalities still could have taken advantage of the program through their states but fretted at the added friction.

The restrictions also raised eyebrows on Capitol Hill, where Sens. Chris Van Hollen (Md.), Elizabeth Warren (Mass.) and five other party leaders wrote the Fed this month to ask it to rethink its criteria, saying it threatens to imperil “hundreds of communities nationwide.”

In response, the Fed said Monday that it would “monitor conditions in primary and secondary markets for municipal securities and will evaluate whether additional measures are needed to support the flow of credit and liquidity to state and local governments.”