Nasdaq OMX Group proposed a "one-time" payout of about $40 million to compensate some financial firms that suffered losses from botched trades during the Facebook IPO .

"We have been embarrassed and certainly we've apologized to the industry" over the Facebook IPO, Nasdaq CEO Robert Greifeld said in an interview with CNBC.

The planned payouts, which involve a mix of cash and trading discounts, will be subject to approval from the U.S. Securities and Exchange Commission .

The amount is far lower than the $100 million or more that the firms said they lost due to the technical problems surrounding Facebook's debut.

The idea of rebates has caused some concern at other exchanges. Sources at Nasdaq rivals said that such a plan would force brokers to trade at Nasdaq, taking market share from competing exchanges.

In a statement, the New York Stock Exchange said "it would be wholly inconsistent with fair practice and an undue burden on competition" to allow Nasdaq to offer such compensation.

"Such a tactic would potentially strongly incent customers to divert order flow to Nasdaq in order to receive compensation to which they are entitled, and allow Nasdaq to reap a benefit from market share gains they would not have otherwise received," the NYSE said. "This is tantamount to forcing the industry to subsidize Nasdaq's missteps and would establish a harmful precedent."

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