By Matt Wirz

The Federal Reserve thawed credit markets in March by promising a whatever-it-takes program to buy corporate bonds. Ten weeks later, the Fed has yet to buy a single bond.

Just the announcement of the backstop ended panic selling, boosted prices and fueled a record surge of new corporate-bond sales. Companies are now reluctant to sign up for Fed purchases because such a move could be seen as a sign of weakness during a market rebound, some bond fund managers and bank executives said.

"I really don't think the market needs it anymore," said Columbia Threadneedle Investments portfolio manager Thomas Murphy. "They are the victim of their own success."

The Fed has yet to officially launch the initiative, which enables it to buy limited amounts of new and pre-existing bonds of companies, in part because it is hashing out the technical details. Only companies that certify they are U.S.-based and haven't received other aid under the Cares Act -- a $2 trillion financial-relief package that includes loans and grants to businesses -- can participate in the program, which would disclose their names, the amount of their bonds that the Fed would purchase and the prices paid.

Those terms "could give bond issuers pause, especially those that already have access to the markets," said Arvind Narayanan, co-head of investment-grade credit at Vanguard Group, which manages $1.8 trillion of fixed-income assets.

The Fed indirectly bolstered corporate-bond prices in May by purchasing $3 billion in shares of exchange-traded bond funds. But that is a fraction of the up to $750 billion earmarked for corporate debt purchases.

The program should be "ready to go by the end of this month," Fed Chairman Jerome Powell said in Senate testimony in May. "I don't say that it won't be a day or two into June, but that's our expectation." A spokeswoman for the Federal Reserve Bank of New York declined to comment beyond Mr. Powell's statement.

Fear of stigma isn't the only thing deterring participation. Some companies don't want the Fed buying their bonds now because that would limit how much the central bank could purchase if another wave of coronavirus roils markets, said one investment banker who covers large U.S. corporations. The Fed can't use more than 1.5% of its backstop funds to lend directly to any single company, according to disclosures by the New York Fed.

Still, the Fed needs to launch the program soon so that it can start making purchases quickly if markets seize up again, Mr. Narayanan said.

Some investors who bought investment-grade bonds in March and April with plans to sell them eventually to the Fed are growing weary of waiting, said Hans Mikkelsen, a bond strategist at Bank of America.

"There is a lot of uncertainty about what the Fed is going to do in the near term," he said.

An unusually large $500 million bundle of investment-grade bonds that traded last week was likely unloaded by one such "tourist" investor, Mr. Mikkelsen said. The portfolio included short-term bonds of such blue-chip companies as Caterpillar Inc. and International Business Machines Corp., which rallied steeply in April and have posted muted gains since.

Caterpillar's 3.9% bond due in 2021 traded at around 103.50 cents on the dollar Tuesday, roughly unchanged from the start of May, according to data from MarketAxess

The Fed also needs to roll out the backstop to ensure its long-term credibility with investors, Mr. Murphy said.

The central bank wants markets to react to policies when they are announced, rather than waiting for them to be enacted, which can take weeks or months. But if it doesn't set up the corporate bond buying facility, investors might second-guess future proclamations, Mr. Murphy said.

Failing to deliver could "reduce the effectiveness of the next thing the Fed announces in the next crisis," he said. "We all know there will be one."

Write to Matt Wirz at matthieu.wirz@wsj.com