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It's time for Jack Dorsey to focus only on Twitter, says big shareholder Steve Ballmer

Former Microsoft CEO and major Twitter shareholder Steve Ballmer told CNBC on Thursday he's been on the phone with Twitter CEO Jack Dorsey, and he thinks it's time to focus full-time on the ailing social media brand.

"Every time I talk to Jack, the message is, 'We need more. More innovation. Move, move, move,'" Ballmer said on "Squawk Box." "Get the cost base right and move forward."

Shares of Twitter tumbled about 10 percent on Thursday morning after the company announced quarterly revenue that was far short of expectations and worse-than-expected forward guidance. Dorsey is also the CEO of Square.

"Running two companies is not the best idea," Ballmer said. "And I'll stand by the notion that Jack's a very creative, innovative guy, as well evidenced by the fact that he started two amazing companies. ... I give him credit for that, and I think now's the time to focus down, at least from my perspective, on the stock I own."

Steve Ballmer
Dan Mescon | CNBC
Steve Ballmer

Ballmer himself stepped down as Microsoft CEO in 2014, amid an uneasy transition into the mobile and hardware industry, saying the company needed a CEO that would be around long term for the company's transformation.

Twitter posted fourth-quarter earnings of 16 cents per share on revenue of $717 million. Analysts expected Twitter to report earnings of 12 cents per share on revenue of $740.1 million, according to a consensus estimate from Thomson Reuters.

Reports have indicated that Twitter might consider selling itself, though no deal has materialized. Ballmer said he still has confidence in Twitter as a company and that it provides a "very valuable service," but there is a lot of volatility in the stock.

"People do have some concerns about revenue," Ballmer said. "I think the company's absolutely got to make more progress."

Ballmer also spoke out on the actions of current Microsoft CEO Satya Nadella, who alongside hundreds of other companies has denounced recent immigration regulations. Ballmer said he thought that outcry over recent immigration orders had conflated two separate issues.