Updated at 2:50 p.m.

Speaking on WGBH’s Boston Public Radio, Boston Mayor Marty Walsh Friday again voiced displeasure with critiques of his administration raised Thursday by City Councilor Michelle Wu around the degree to which Walsh has used privately raised funds to pay for emergency relief efforts.

During her own appearance on BPR Thursday, Wu said that while she has no problem with philanthropy, the control exercised by the Walsh administration over which organizations are receiving tens of millions of dollars in private donations raises at least the potential for conflict of interest.

"To be clear: our communities need support. In many cases, it’s a matter of life or death," Wu said in a statement following her conversation with Jim Braude and Jared Bowen Thursday. "But using the platform of city government to direct private fundraising in this way creates conflicts of interest under a troubling lack of oversight."

Walsh has established two major funds to funnel charitable donations through City Hall: the Boston Resiliency Fund, which has raised some $33 million, about $27 million of which has been awarded to Boston nonprofits — half of which, Walsh said, are led by people of color; and a new Racial Equity Fund, which will award grants to nonprofits working to dismantle racism in the city.

During an already-scheduled press conference held shortly after Wu’s radio appearance Thursday, Walsh responded with a sharp rebuke of the councilor.

Without naming Wu, Walsh said that “people” should “take a little of their time to learn how the fund was set up and maybe help us get more money for the fund rather than Monday morning quarterback on a radio show.”

Asked about those remarks on BPR Friday, Walsh said he did not intend to “get into a debate with someone’s opinion” about the fund, adding that the “someone” in question “doesn’t understand what the fund was set up to do.”

But Walsh did defend the integrity of the funds in question, noting that the Boston Resiliency Fund was established in a moment of crisis and has paid for everything from emergency food programs to Chromebooks for Boston Public School students to expanded COVID-19 testing in Boston Community Centers around the city.

Walsh also implied that Wu’s motivations for criticizing him were political. Wu is widely considered to be a potential mayoral candidate next year.

“This is a time to really work together and not play politics,” Walsh said.

Wu has not said she intends to run for mayor in 2021, nor has Walsh stated he intends to run for re-election, though he strongly hinted on-air Friday that he is.

“What do you think I’m doing?” Walsh chuckled. “I love my job. ... I think you can figure it out.”

The mayor also told Jim and Jared that he is looking at police overtime, though he added that he is limited in what he can say publicly because it could put the city at a disadvantage in ongoing negotiations. The issue has long been controversial because some police officers have earned overtime and private detail pay that puts their earnings far above the mayor’s own salary.

“What I’m going to be looking at is how do we come up with ways of working on [overtime] in collective bargaining, is there an opportunity for us to look at that,” Walsh said. “There are some reforms you can get out of the contract, but a lot of reforms people are looking for, it’s in training, it’s in how the police department is run.”

Walsh also called for Gov. Baker and the state legislature to extend a partial moratorium on evictions, saying that many residents are still out of work due to no fault of their own, and that he fears mass evictions if the state doesn't act soon.

As mayor, Walsh does not have authority to order such a moratorium himself, but he has prohibited evictions of residents of Boston Housing Authority homes through the end of the year.