Deaths keep falling in N.Y. and N.J. as reopening plans take shape.

Gov. Andrew M. Cuomo said on Monday that 337 more people had died of the virus in New York State, and Gov. Philip D. Murphy of New Jersey reported an additional 106 deaths.

The one-day tolls were less than half of what the two states reported at their peaks.

With both states showing progress in fighting the virus, Mr. Cuomo and Mr. Murphy have begun to offer details on reopening in the months ahead.

On Sunday, Mr. Cuomo said that after May 15, when his order shutting down New York is set to expire, businesses in what he called low-risk industries like construction and manufacturing might begin to reopen in parts of the state that have been less affected.

The shutdown order will be extended beyond May 15 in many parts of the state, Mr. Cuomo said on Monday.