NEW YORK — Under fire over his management of the coronavirus’ lethal path through New York’s nursing homes, Gov. Andrew Cuomo said Monday the state didn’t cover up deaths but should have moved faster to release some information sought by lawmakers, the public and the press.

“All the deaths in the nursing homes and hospitals were always fully, publicly and accurately reported,” the Democratic governor said, weeks after the state was forced to acknowledge that its count of nursing home deaths excluded thousands of residents who perished after being taken to hospitals. He explained the matter Monday as a difference of “categorization,” with the state counting where deaths occurred and others seeking total deaths of nursing home residents, regardless of the location.

“We should have done a better job of providing as much information as we could as quickly as we could,” he said at a virtual news conference. “No excuses: I accept responsibility for that.”

Cuomo, who has seen his image as a pandemic-taming leader dented by a series of disclosures involving nursing homes in recent weeks, said he would propose reforms involving nursing homes and hospitals in the upcoming state budget, without giving details.

But he continued to blame a “toxic political environment,” and “disinformation” for much of the complaints surrounding his administration’s handling of the issue.

The governor’s comments didn’t satisfy state Assemblyman Ron Kim, a Democrat and outspoken critic of the administration’s approach to nursing homes during the pandemic. Kim’s uncle died of a presumed case of COVID-19 in a New York nursing home in April.

“I didn’t think it was much of an apology,” Kim said. “It doesn’t pass the smell test.

“But what gets lost, ultimately, is: If they were transparent, if they did disclose everything in real time, we could have had different policies, and that would have had a different outcome in how we protected our communities.”

The head of a major association of New York nursing homes said the state erred by focusing too much on hospitals early in the pandemic and leaving nursing homes “scrambling to safeguard their residents and staff.”