Hospital Corp. of America, the nation's largest for-profit hospital chain, and American Hospital Supply Co., the largest provider of hospital supplies, yesterday indefinitely postponed their repsective stockholder votes on the proposed acquisition of American by HCA.

The companies postponed their stockholder votes because a competing $3.6 billion bid for American by Baxter Travenol Laboratories Inc. has received the support of many American shareholders. Baxter is offering $50 a share in cash for half of American's outstanding stock and $50 a share in Baxter stock for the other half. Under terms of the proposed merger between HCA and American, each American share would be converted into three-quarters of a share of a new holding company that would own HCA and American, making the offer worth about $36 a share to American stockolders.

Wall Street analysts say it is unlikely that the plan will be approved by American stockholders because HCA's offer appears to be worth significantly less than Baxter's.

American, which has been critical of Baxter's takeover attempt, said it plans to hold a special board meeting on July 12 to consider Baxter's latest unsolicited bid.

"Baxter's attempt to acquire American is a desperation move thrown together at the last minute without the kind of thorough analysis necessary to see such a transaction through," American Chairman Karl D. Bays said yesterday. "Their apparent failure to take into full account the antitrust implications of combining the two companies raises questions about the adequacy of their preparation. Moreover, we believe Baxter's campaign against the HCA merger, without filing proxy material with the SEC, raises serious legal questions."

Baxter denounced Bays' remarks almost as soon as he made them yesterday. "The statement issued by American Hospital Supply earlier today is yet another smoke screen designed to divert attention from the real issue: how Baxter's $50-a-share proposal can possibly be less attractive than $35 a share," Baxter said.

Baxter, best known for supplying hospitals with intravenous solutions, is a smaller comapny than HCA or American. It had revenue of $1.8 billion and net income of $29.1 million last year. HCA had revenue of $4.2 billion and net income of $296.8 million last year, while American had revenue of $3.5 billion and net income of $237.8 million.

HCA, which has not said much since Baxter entered the bidding war for American, said yesterday that the company has serious quesitions about "the legality and ethics of Baxter's intervention in HCA's pending merger with American. HCA fully intends to protect its rights under the HCA-American merger agreement and to support American's efforts to serve the best interests of its stockholders."

American, which has said it believes a merger with HCA is in the company's long-run best interest, said yesterday it does not believe Baxter's offer is really worth $50 a share. "Baxter has overstated the value of its proposal at every turn," American said.

"Management believes that Baxter's long-term performance prospects are poor and questions the quality of its recent earnings performance," American said. "During 1984, Baxter's net earnings declined 87 percent. . . . No one should assume that a transaction with Baxter will result or that the exchange ratio in American's merger with HCA will change."