May 10 (Reuters) - Oil leaked into the Hudson River on Sunday after a transformer fire and explosion a day earlier at the Indian Point nuclear plant north of New York City, and Governor Andrew Cuomo said he was concerned about environmental damage.

Cuomo visited the plant for a briefing on Sunday. The governor, who in the past has called for the plant to be shut down because of its proximity to densely populated New York City, also visited the plant on Saturday.

When the transformer exploded, it released oil into a holding tank, which then overflowed, sending oil onto the ground and into the river, Cuomo told reporters on Sunday after he was briefed by emergency and plant officials.

He said crews were working to contain and clean up the oil spill but it was not clear yet how much oil had been released.

"If you are on site, you see an oil sheen all over the area where the transformer went on fire, and it was a significant area that was covered by oil, foam and water," Cuomo said.

The transformer explosion and fire at the nuclear power reactor 40 miles (65 km) north of New York City was quickly put out. The fire triggered the closure of the plant's Unit 3 reactor, while the other Unit 2 reactor continued to operate.

Entergy Corp, which runs the facility and is one of the largest U.S. nuclear power operators, said the plant was stable and there was no danger to the public or to employees.

"Anything that happens at this plant obviously raises concerns," due to the proximity to the largest U.S. city, Cuomo said.

"The transformer fire in and of itself was not dangerous. But the fear is always that one situation is going to trigger another. If something goes wrong here, it goes very wrong for a lot of people."

Cuomo said emergency crews thought the fire was out but it reignited and had to be extinguished again.

The transformers are located around 300-400 feet (90-120 meters) away from the reactor.

The plant, which dates back to the 1960s, has around 1,000 employees.

It is one of 99 nuclear power plants licensed to operate in the United States and which generate about 20 percent of U.S. electricity use, according to the Nuclear Regulatory Commission's website. (Reporting by Fiona Ortiz in Chicago; Editing by Chris Reese)