Google, Facebook Inc. and other tech giants have long tinkered with ways to grow outside the core businesses they dominate. Now those efforts are becoming urgent.

Facebook Chief Executive Mark Zuckerberg, beset by public anger over abuses on the social network, spent the company’s annual developer conference last week talking up his vision for a Facebook more focused on private messaging and small groups than on the advertising-driven social-media hub that gained it nearly 2.4 billion monthly users.

Messaging is one of several areas Facebook has been eyeing for new opportunities. Another got the spotlight last week when The Wall Street Journal reported that Facebook is recruiting financial firms and online merchants to help launch a cryptocurrency-based payments system.

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Apple Inc., meanwhile, said last week its sales-and-profit slump extended into a second straight quarter—the first time that has happened in more than two years—thanks to falling sales of the iPhone, the product that turned it into a colossus. Its response has been to try to morph itself into a services company fueled by app and entertainment sales as much as hardware.

Google parent Alphabet Inc. has been Big Tech’s most eclectic big-idea factory. It has worked on self-driving cars for a decade and has arms devoted to everything from balloon-tethered internet access to extending human life. But it has had little success turning those efforts into moneymaking businesses. Advertising is still 85% of its revenue, and operating losses at its “other bets” segment ballooned by 52% in the last quarter to $868 million, Alphabet said last week. The perils of its ad dependence were laid bare when an unexpected drop in quarterly sales sent Alphabet shares down 7.5% on Tuesday, their biggest one-day drop since 2012.

A confluence of forces is behind Big Tech’s business-model ferment. Blowback over privacy abuses and misinformation threatens ad-driven strategies at Facebook and Google built on harvesting people’s information and maximizing the time they spend glued to the internet. The smartphone, which underpinned so much of the tech industry’s boom over the past decade, is maturing, with incremental innovation and flagging sales.

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And the law of large numbers, combined with the tech industry’s history of upstarts leapfrogging incumbents on innovation, compels executives to seek out new places to disrupt, lest they themselves be disrupted.

“Their perspective is: We have to keep the growth,” says Tim Kendall, a former senior executive at Facebook and Pinterest Inc. who now runs Moment, an app to help manage smartphone use. Mr. Kendall says the need to diversify is all the greater because regulatory concerns make it risky for giants to bet on growing their share of the markets they already dominate. “The current regulatory climate is such that all of them are saying, ‘We can’t acquire growth into our core business because the [Federal Trade Commission] will block it.’”

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Mr. Zuckerberg in an interview with the Journal last week emphasized the significance of Facebook’s changes, calling his plan to build out less-public communication networks “the beginning of a new chapter” and attributing some of the recent executive departures to the magnitude of the switch.

Click here for more from The Wall Street Journal, where this story first appeared.