By Yoree Koh 

Some of Twitter Inc.'s biggest and earliest backers said they don't intend to sell shares when rules barring them to do so expire on May 5, giving the young public company a much-needed vote of confidence after its shares tumbled in recent months.

Rizvi Traverse Management LLC, whose 14.4% stake in the company is the largest, does not plan to sell, according to a person familiar with the company's thinking. The person said the firm believes in the long-term strategy and power of the short-messaging platform.

A spokesman for J.P. Morgan Asset Management said the firm does not intend to sell its shares on May 5. The firm holds 8.4% of the company's shares, the second-highest stake. Most of J.P. Morgan's shares are managed by entities related to Rizvi.

Those statements followed Twitter's disclosure, in a Monday filing with Securities and Exchange Commission, that two of its co-founders, Jack Dorsey and Evan Williams as well as its CEO Dick Costolo have no plans to sell any of their company shares. The three men have a combined 14.8% stake in the San Francisco-based company.

Twitter added that Benchmark Capital would not sell, or distribute to its investors, any of its 5.4% stake on May 5 either.

"We back entrepreneurs who are making a big impact in the world. This was true of Twitter when it was a 25-person start up and it is true now, " said Matt Cohler, a general partner at Benchmark Capital, in an interview. Peter Fenton, another general partner at Benchmark, serves on Twitter's board of directors.

Collectively, the statements would place about 34% of Twitter's shares off-limits when the lock-up expires, in the first opportunity for Twitter executives, directors and large investors to cash out. Some 474.4 million Twitter shares could be freed to the market on May 5.

The decisions from Twitter's biggest investors come after a troubling couple of months in which shares fell as investors worried about user growth and Twitter's ad business. In less than two months after the company's Wall Street debut in November, Twitter shares soared as high as $74.73, from their IPO price of $26. But they've tumbled about 37% so far this year. Monday, shares rose 82 cents, or 2.05%, to $40.87.

Twitter said Monday that if Messrs. Dorsey, Williams or Costolo decide to sell, they are required to do so under a prescribed trading plan. The company said its policies require a "cooling off" period in trading plans, so executives have to wait at least 90 days to sell stock after signaling an intent to do so.

Mr. Williams owns 9.4% of the stock, Mr. Dorsey has 4% and Mr. Costolo has 1.4%, according to Twitter's annual proxy filed last week. None of the three sold any of their shares when the company went public last year.

Twitter employees had their first chance to sell a limited quantity of shares in February. That batch was small, covering just 1.8% of outstanding shares and was mainly to give non-executive employees a way to settle income-tax expenses from vesting shares. More of their shares will become eligible for sale on May 5.

George Stahl contributed to this article.

Write to Yoree Koh at yoree.koh@wsj.com

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