The Democratic leaders of the New York State Senate are moving to strip Gov. Andrew M. Cuomo of unilateral emergency powers granted during the pandemic, setting up a remarkable rebuke for the governor from members of his own party.

The Senate’s measures, which could be voted on as soon as next week, underscore the deepening division between Mr. Cuomo and state lawmakers since the governor admitted to intentionally withholding critical data on virus-related deaths from the Legislature.

The moves came even as it emerged that the F.B.I. and the U.S. attorney for the Eastern District of New York had opened an inquiry into the Cuomo administration’s handling of nursing homes during the pandemic. It was not known whether the inquiry, which was confirmed by three people familiar with the matter, was focused on Mr. Cuomo or any individual, only that it was in it earliest stages.