“Alarming’’ levels of radioactivity have been discovered in three monitoring wells at the Indian Point nuclear power plant, Gov. Cuomo said Saturday.

He told the state Departments of Health and Environmental Conservation to investigate how “radioactive tritium-contaminated water’’ leaked into the groundwater at the plant, in the Hudson River town of Buchanan in northern Westchester County.

In letters to the agencies, Cuomo said the radioactive water has not gone beyond the boundaries of the plant and poses no immediate threat.

The leak was discovered by the plant’s owner, Entergy.

The governor has made repeated calls for the closing of Indian Point, which produces power equal to 30 percent of the city’s electricity.

He cited concerns ranging from a terror attack to a possible earthquake to sturgeon dying in the Hudson because of the warm water the plant discharges.

But the governor supports keeping open two other nuclear plants, which are farther upstate.

Cuomo, who lives in the Westchester town of New Castle, described as “unacceptable’’ the latest problem at the nuke plant, which has experienced a number of unplanned shutdowns last year.