Investors are ratcheting up the pressure on Watertown-based athenahealth to consider a sale, arguing that the publicly traded health care information technology company might operate more efficiently under private ownership.

Elliott Management Corp., the New York hedge fund that has offered to buy athenahealth for nearly $7 billion, wrote to the company’s board of directors Thursday that other shareholders share its frustration with how the company has performed.

“Athenahealth’s shareholders have spoken, and it is clear from their words and actions that rejecting the idea of evaluating a sale and instead offering assurances that the company has a standalone plan for getting back on track will not be accepted,’’ the letter said.

Last week, athenahealth’s largest shareholder, Janus Henderson Group, weighed in, saying it “believes initiating a formal sale process . . . is in the best interest of . . . shareholders.’’

The statement, in a regulatory filing, said Janus Henderson had also told athenahealth’s board that it was concerned about the company’s “execution of strategic initiatives.’’ The investment fund owns nearly 12 percent of athenahealth’s shares, while Elliott owns about 9 percent.

Elliott has made similar criticisms on topics including the company’s sales, service, product selection, and level of management turnover. In the year before Elliott announced its buyout bid, athenahealth shares increased 48 percent, compared with more than 80 percent over the same period for the major benchmark stock index.

In a statement Thursday afternoon, athenahealth said it is continuing to review Elliott’s offer, but it also criticized the hedge fund’s “attempts to publicly pressure the Board and management team.’’

“Based on our discussions with shareholders, we do not believe the positions set forth in Elliott Management’s letter are representative of the positions of all of our shareholders,’’ the statement said.

Athenahealth stock fell slightly in Thursday trading, down 15 cents to $153.45.

A sale of the company to Elliott or another buyer would create uncertainty for Jonathan Bush, the company’s cofounder and chief executive. Elliott and athenahealth have been in discussions for months, and the hedge fund said athenahealth already rebuffed one takeover offer.

Bush has given up his title of chairman and has said he will step aside as president.

The company last year cut about 500 jobs, or 9 percent of its global staff.

Athenahealth is a major employer in Watertown, with 2,000 ­workers concentrated in the Arsenal on the Charles project that is being developed around its headquarters.

Andy Rosen can be reached at andrew.rosen@globe.com.