Updates May 1 story with quotes from Friday's investor call in paragraphs 4-5, details on offshore wind projects

May 2 (Reuters) - Eversource Energy ES.N reported a rise in first-quarter profit on Thursday, as the U.S. electric and water utility benefited from higher electricity rates.

Regulated utilities use rate case proceedings to seek power price increases, basing their appeals on their investments or expenses incurred in delivering services.

Quarterly earnings from Eversource's electric distribution segment rose 12.1% to $188.4 million from a year earlier, while the New England utility earned $199.4 million from its electric transmission segment, a year-over-year increase of 12.8%.

Eversource Energy supplies electricity and natural gas to about 4 million customers across Connecticut, Massachusetts and New Hampshire. The company exited its role in offshore wind development last year, but it is overseeing construction of an onshore substation for the Revolution Wind project that is in the works off the shores of Rhode Island.

"The onshore substation is the critical path to the project going into service," Eversource CEO John Nolan said on the company's earnings call on Friday.

"We continue to monitor the project's overall construction progress closely, currently in the latest construction updates, the cost estimates we have been provided," he said.

U.S. offshore wind projects have been under threat by the administration of President Donald Trump, who has ordered the halting of a New York offshore wind farm and announced tariffs that raise costs for the projects.

Eversource's project, Nolan said, is proceeding as planned.

While the company reported higher profits tied to its power segment, earnings from Eversource's water distribution segment were down 33.3% to $3.6 million from last year.

In January, Eversource agreed to sell its public water supply unit, Aquarion Water, it acquired in 2017 in a deal worth $2.4 billion, as the utility firm aims to pare debt and focus on its primary electricity and natural gas businesses.

Eversource reported a net income attributable to common shareholders of $550.8 million for the quarter ended March 31, up 5.5% from a year earlier.

(Reporting by Tanay Dhumal in Bengaluru and Laila Kearney in New York; Editing by Alan Barona and Tomasz Janowski)

((Tanay.Dhumal@thomsonreuters.com; Twitter: https://twitter.com/TanayDhumal))