Mr. Cuomo’s office has a keen, if unsubtle, eye for the moment: The announcement coincides with the women’s marches in Washington, New York and other cities across the country, where Mr. Trump’s inauguration is expected to pull hundreds of thousands of women into the streets.

And it caps a two-week period in which the governor unveiled an agenda that seemed to aim at every liberal mark, such as criminal justice reform, college tuition assistance, renewable energy plans and child care tax credits. The rollout was an undisguised retort to the nascent Trump presidency, sounding to some like the opening moments of a potential Cuomo presidential run. But his leftward tilt has not muted some liberal activists’ complaints that Mr. Cuomo has not worked hard enough to establish a Democratic majority in the State Senate, which, in Republican hands, has blocked significant liberal legislation in the past.

With this part of Mr. Cuomo’s agenda, at least, there will be no need for a legislative blessing. The administration is issuing the regulations under a law that authorizes the Financial Services Department to set standards for insurers, said Alphonso David, the governor’s counsel. Once they are filed, the regulations will take effect in about two months.

“We want women to know that even if there are changes in federal law, there aren’t going to be any disruptions to their coverage here in New York,” Mr. David said.

The governor’s office estimates that 4.5 million New Yorkers, about half of them women, are covered by commercial insurance policies governed by the new regulations. His aides could not say how many of those women would feel a direct impact.