With the number of new deaths and rate of hospitalizations falling in New York, Gov. Andrew M. Cuomo said on Monday that “the worst is over” in the coronavirus pandemic, and he announced an alliance with six other Northeastern governors to explore how to eventually lift restrictions — a move that appeared to be an implicit rebuke to President Trump.

The governors from New Jersey, Connecticut, Pennsylvania, Delaware, Massachusetts and Rhode Island said they would begin to draw up a plan for when to reopen businesses and schools, and how quickly to allow people to return to work safely, although the timeline for such a plan remained unclear.

“If you do it wrong, it can backfire, and we’ve seen that with other places in the globe,” Mr. Cuomo said. “What the art form is going to be here is doing that smartly and doing that in a coordinated way.”

The joint effort was the first of two announced on Monday: The governors of California, Oregon and Washington, three Western states that were among those that felt the impact of the virus before it spread rapidly in the Northeast, announced a similar pact. All but one of the 10 governors on the two coasts are Democrats.