BOSTON — A petition signed by 21 antitrust experts and health economists asks a Massachusetts judge to block efforts by the state’s biggest health care system to absorb three more hospitals.

The Partners HealthCare System’s planned takeovers of South Shore Hospital and two Hallmark Health System hospitals have been approved by Attorney General Martha Coakley under certain conditions.

The petition signed by antitrust specialists, many from major U.S. universities, says the deal is unlikely to contain rising medical costs as intended, according to The Boston Globe.

“We do not believe that the proposed restrictions on Partners’ conduct included in the (settlement) will offset the consumer harm that is likely to arise from the acquisitions of South Shore and Hallmark hospitals and their physician affiliates,” they wrote to Judge Janet Sanders, who is weighing whether to approve the agreement.

She has extended a public comment period through Sept. 15 and scheduled a Sept. 29 hearing on the matter.

None of the petition signers has a financial stake in the deal.

Partners operates Brigham and Women’s and Massachusetts General hospitals, as well as several community hospitals, health centers, and a health plan.

Under Coakley’s deal, Partners would be allowed to complete the acquisitions, but in exchange must put a seven-year freeze on additional takeovers; limit price increases across its network to the rate of general inflation for 6 1/2 years; and calls for an outside monitor to gauge Partners’ compliance for 10 years.

Coakley defended the deal.

“We are confident that this (settlement) does more to control health costs for consumers and alter Partners’ business practices than any lawsuit would have potentially achieved,” spokesman Brad Puffer said.