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On a late August morning, Kevin Systrom, chief executive of Instagram, took an oath before testifying at a hearing of the California Corporations Department, which sought to determine if Facebook’s acquisition of the photo sharing service was in the best interest of Instagram investors. Facebook requested the hearing as a way to speed up the approval of its acquisition.

When asked if his company had received any offers besides Facebook’s at the time of the negotiations, Mr. Systrom said, “No, we never received any offers,” according to transcripts of the hearings. He said Instagram had “talked to other parties, but never received any formal offers from anybody else.”

Ivan V. Griswold, a lawyer for the state regulators, asked again: “Immediately before the negotiations, did you receive any offers from invest — .” Before he could finish his question, the transcripts show, Mr. Systrom cut him off.

“We never received any formal offers or term sheets,” Mr. Systrom said. “No.”

Yet the accounts of several people close to Twitter and Facebook, and documents reviewed by The New York Times, contradict the statements he made under oath. Mr. Systrom and Mike Krieger, the other founder of Instagram, held several meetings as late as March with top Twitter executives, according to people on both sides of the talks, who requested anonymity because the talks were private and because they were concerned about legal repercussions. These people said the sides had verbally agreed weeks earlier on a price for Instagram of $525 million in cash and Twitter shares.

Mr. Systrom told Twitter on March 20 that he and Mr. Krieger had thought about the offer and had decided to “remain independent.” Less than three weeks later, Twitter found out, along with the rest of the world, that Instagram had agreed to be acquired by Facebook in a $1 billion deal negotiated personally by Facebook’s chief executive, Mark Zuckerberg. The deal included $300 million in cash and the rest was in Facebook stock. Instagram was privately owned by its founders, Mr. Systrom and Mr. Krieger, who had a majority stake in the company, and several venture capital funds.

The people familiar with the negotiations said Twitter executives were shocked that they had not been given an opportunity to present a counteroffer. They said Twitter was prepared to make higher offers.

Facebook and Mr. Systrom declined to comment about the statements made to regulators or the talks with Twitter. Gabriel Stricker, a Twitter spokesman, also declined to comment.

Although it might seem unimportant whether wealthy investors made a few million dollars less than they could have, those investors often represent funds that include workers’ pensions and mutual funds. The case could also be seen as another example of a large tech company’s sidestepping regulators.

Statements made by other people involved in the Instagram deal don’t add up, either. When Facebook submitted its applications to California regulators, its general counsel, Ted Ullyot, wrote that although the board had considered possible alternatives, there was a “lack of interest in acquiring the company expressed by other potential acquirers of the company.” Through a spokesman, Facebook declined to comment.

Mark Leyes, director of communications for the Corporations Department, said the department — which is to protect consumers and investors from self-dealing in transactions — had “not received any complaints or protests of our original fairness hearing proceedings in the Facebook/Instagram acquisition.”

In general, said Eric Talley, a law professor at the University of California, Berkeley, “if there is sworn testimony, there are perjury risks.” Also, he added, “there are fraud risks in which an inaccurate statement to your investors could violate antifraud laws at both the state or federal level.”

Dr. Talley said there were many reasons people might try to hide information from investors, including “deal sweeteners,” in which someone might be allowed to remain head of a company or be given more cash.

Mr. Systrom, who previously worked on mergers and acquisitions at Google, was careful about his interactions with Twitter from the start. He asked to meet in restaurants around San Francisco, rather than in either company’s office, according to people briefed on the talks. When he was handed the term sheet by a Twitter employee, a nonbinding document outlining the terms of a proposed acquisition, he read it and then handed it back, asking Twitter executives to hold onto it over the weekend as he weighed the details, those people said.

It is possible investors would have been better off selling in an open auction, to Twitter or even to Google or Microsoft.

The deal with Facebook closed at $735 million in early September, after Facebook’s stock plunged because of investors’ fears that its revenue growth prospects were weak. Given that the privately traded Twitter is expected to make $1 billion in revenue next year, which would increase its valuation considerably, Instagram investors might have made millions of more dollars.

It is unclear why Facebook didn’t mention Twitter’s interest. A clue might be found in the company’s amended S-1 filing with the Securities and Exchange Commission, outlining details of the Instagram acquisition: Dr. Talley said it used language often reserved for antitrust cases.

The wording in the updated S-1 filing, which included a termination fee of 20 percent if the deal fell through, “suggests that there really was some concern about antitrust clearance from the F.T.C.,” Dr. Talley said, referring to the Federal Trade Commission. “These antitrust questions would not have been raised if Instagram was selling to Twitter or Google.”

An F.T.C. spokesman, Mitchell J. Katz, declined to comment.

There also is the issue of what Mr. Systrom and regulators consider a “formal offer.” Although lawyers make differing arguments, Mr. Systrom was asked by regulators on several occasions if he had received other offers, formal or otherwise, and each time he said no.

Facebook has tangled with regulators before. What it does with its customers’ data attracted the attention of the F.T.C., which accused it last year of “unfair and deceptive” practices. The agency’s settlement with the company required Facebook to submit to privacy audits for 20 years.

Facebook has also sparred with the S.E.C. over its depiction of its mobile strategy in its filing to go public.

At the end of the hearing, regulators asked Mr. Systrom a third time about other offers: if there had been “any other inquiries from third parties about a possible acquisition of Instagram” after the Facebook deal was announced. Although Twitter executives had since tried to contact Mr. Systrom, he replied, “I and the board have not received any.”

E-mail: bilton@nytimes.com