Richmond City Council on Wednesday informally agreed to steer $500,000 from a ballooning surplus into a COVID-19 relief fund, with a potential for the money to provide emergency aid for city residents in desperate circumstances.

The move came as the City Council majority rejected a recommendation from Mayor Levar M. Stoney to use the one-time dollars to pilot initiatives aimed at reducing gun violence, improving mental health services and cutting the higher infant and maternal mortality rates among African-Americans.

Council members worried about whether the funding to continue the programs would be available once the initial money runs out.

Fifth District Councilwoman Stephanie A. Lynch helped gain the money for the COVID-19 relief fund after telling members that she is besieged with pleas from people who need immediate help paying for food or shelter.

She said the city’s funding for emergency relief has dried up, leaving dozens of struggling families and individuals with no place to turn.

The debate over use of the money followed the Stoney administration’s disclosure Monday that the surplus from the 2019-20 fiscal year that ended June 30 had grown to $18.9 million, an increase of $5.2 million from the $13.5 million surplus originally reported.

The increase was attributed to better than expected collec- tions of sales, meals and personal property taxes and of business license revenue, indicating the resilience of the city’s economy in the face of the pandemic.

Most of the unspent dollars already were spoken for, with more than $7 million going to untouchable savings and another $5.5 million earmarked for a fund to pay for maintenance and repairs to city buildings and other infrastructure.

The council adopted two other mayoral recommendations, including steering $5.78 million into a trust fund to help cover health insurance and other benefits for retirees other than the pension.

A new audit report has indicated the mayor and the council are facing an increasing liability for those retirement benefits called OPEB, which has long been underfunded. According to Finance Director John Wack, the city will need to set aside about $15 million in the coming 2021-22 budget to address the growing OPEB bill and to shore up its pension fund that also is underfunded.

The council also agreed with the mayor’s proposal to spend $110,000 for an equity study of city operations and policies.