Carl Icahn has a significant stake in Southwest Gas Holdings Inc. and is pushing the Nevada utility to abandon a potential acquisition and focus on improving its share price instead, according to a letter he sent to the company that was viewed by The Wall Street Journal.

The letter was sent to Southwest’s board Monday, a day after a Reuters report that the company could complete a deal to buy Dominion Energy Inc.’s Questar Pipeline Co. for around $2 billion including debt as soon as this week.

Southwest’s...

Carl Icahn has a significant stake in Southwest Gas Holdings Inc. and is pushing the Nevada utility to abandon a potential acquisition and focus on improving its share price instead, according to a letter he sent to the company that was viewed by The Wall Street Journal.

The letter was sent to Southwest’s board Monday, a day after a Reuters report that the company could complete a deal to buy Dominion Energy Inc.’s Questar Pipeline Co. for around $2 billion including debt as soon as this week.

Southwest’s shares fell 2.5% Monday, giving the company a market value of roughly $3.9 billion. The shares traded for more than $90 apiece two years ago. The Las Vegas company serves more than 2 million customers in Arizona, Nevada and California.

Mr. Icahn, whose son Brett now works alongside him, said in the letter that the purchase of Questar for that price would be a huge mistake and diminish shareholder value.

“But even if you were not overpaying, this is no time for management with the many problems you have (including with regulators) to embark on a major new investment especially when you have shown an inability to manage and control what you already own,” the octogenarian investor wrote. He said in the letter he tried to reach the company and hasn’t heard back.

Southwest officials couldn’t immediately be reached for comment Tuesday morning. Dominion declined to comment.

He said the company’s shares have underperformed its regulated gas-utility peers, its expenses have increased and there has been little turnover on its board.

Mr. Icahn said the company’s shares, with the proper changes, could appreciate 75%.

Warren Buffett’s Berkshire Hathaway Inc. had agreed to buy Questar, a natural-gas pipeline company that provides transportation and storage service, for around $1.7 billion including debt. The parties abandoned the deal in July because of uncertainty over whether it would be cleared by regulators. Dominion said at the time it was initiating a sale process for Questar and aimed to close a deal by the end of the year.

Mr. Icahn has agitated at other utilities, including FirstEnergy Corp. earlier this year. He now holds seats on the Ohio utility’s board.

Write to Cara Lombardo at cara.lombardo@wsj.com