An image of Mark Zuckerberg, left, with Robert Greifeld, chief executive officer of Nasdaq, right, remotely ringing the opening bell for trading is projected on a screen at the Nasdaq MarketSite in New York in 2012. (Peter Foley/Bloomberg)

Nasdaq has agreed to pay $10 million, the largest penalty ever lodged against an exchange, to settle civil charges concerning its handling of Facebook’s market debut a year ago, which was marred by technical problems.

In an order released Wednesday, the Securities and Exchange Commission accused Nasdaq of failing to ensure that its systems were running properly for Facebook’s initial public offering on May 18, 2012. It also alleged that the exchange’s senior officials made a series of “ill-fated” decisions that violated the exchange’s self-imposed rules.

Nasdaq’s technology became overwhelmed by the huge volume of requests to buy, sell or cancel orders for Facebook shares that day, the SEC said. As a result, 19 minutes’ worth of orders — or 30,000 orders — got stuck in the system and did not reach the market for more than two hours, causing a huge disruption and tens of millions of dollars in investor losses.

The exchange’s leadership team recognized that there was a problem but decided to initiate trading anyway because it thought it had fixed the issues. The SEC said that Nasdaq did not understand the precise cause of the error when it made that decision.

The exchange then ended up buying 3 million Facebook shares to cover for the imbalance between buy and sell orders during the 19-minute lag time, even though there was no rule allowing the exchange to make such a purchase, the SEC said.

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“This action against Nasdaq tells the tale of how poorly designed systems and hasty decision-making not only disrupted one of the largest IPOs in history, but produced serious and pervasive violations of fundamental rules governing our markets,” George S. Canellos, co-director of the SEC’s enforcement division, said in a statement.

Nasdaq agreed to settle the case without admitting wrongdoing.

The exchange’s parent company, Nasdaq OMX Group, already planned to pay qualified customers $62 million total to make up for losses. The settlement with the SEC is “another important step forward,” said Robert Greifeld, the company’s chief executive.

In a letter posted on Nasdaq’s Web site, Greifeld said the exchange had conducted more than 100 IPOs without incident before Facebook’s debut. “While we prepared extensively for the Facebook initial public offering, including thorough tests of our systems with member firms, the challenges we encountered that day were unprecedented,” Greifeld wrote.

Nasdaq has since put in place several trading safeguards, he said.

The first-ever penalty imposed by the SEC against an exchange occurred last year, when the New York Stock Exchange agreed to pay $5 million to settle charges that it provided real-time market information to proprietary customers before distributing it to the public at large, violating regulations that require fair access to market data.

The SEC also was investigating whether Facebook and its underwriters — led by Morgan Stanley — selectively disclosed information immediately before the IPO about Facebook’s money-making prospects. But the agency did not address that aspect of the probe Wednesday or confirm whether the investigation is ongoing.

Since its IPO, Facebook has spent the past year battling concerns about whether it can make money and keep its more than 1 billion users tethered to the social network. The company’s stock price has recovered some of its worst losses, though it has not rebounded to the $38 per share it hit on its market debut.

A number of factors, including investor doubts about its advertising model, might have contributed to the slack, but some have said the company’s IPO left a black mark on the stock.

Facebook has taken several steps in the past year to attract advertisers and improve its products on smartphones and tablets, including redesigning the site to make it easier to navigate through friends’ posts and to look at ads on smaller screens.

Since the IPO, Facebook itself has lost about $75 billion in market capitalization, down to $50 billion Wednesday from a value of $104.2 billion when the market closed on its opening day of trading.

(The Washington Post Co. chairman and chief executive Donald E. Graham is a member of Facebook’s board of directors.)

Hayley Tsukayama contributed to this report.