Families are caught in a vacuum of information, barred from visiting, and nursing homes have a financial incentive to provide only the most benign view of what is happening behind their closed doors.

On Thursday, Gov. Andrew M. Cuomo, responding to the outcry of families, promised an executive order requiring nursing homes to inform relatives about Covid-19 infections and deaths in the facilities.

He also pledged to release information for each nursing home, “to the best we have,” something the state had previously declined to do.

Sapphire’s administrator, Jerry Enella, did not respond to repeated messages on Wednesday and Thursday. On its website, the home says: “We strive to provide the highest quality of care to each of our patients by offering a range of services to meet your needs. Our goal is to keep you as healthy as possible by offering care when you need us most.”

Mr. Kim, the state assemblyman, said he had a heated exchange with Mr. Enella outside Sapphire on Wednesday afternoon. Mr. Enella, he said, defended the quality of care and told Mr. Kim that there were 29 deaths there, one of the highest totals in the region so far.

“It was very clear that the director was not able to handle the situation,” Mr. Kim said afterward. “We went to lend a hand and understand what they need. But they’re all about trying to get damage control and protect themselves.”

On Thursday, State Health Department officials were on the site doing a survey and evaluating conditions at the home, said Michael A.L. Balboni, a former state senator who is a consultant for the Sapphire Care Group.