Google delayed its plan to scrap a widely used technology to track web-browsing habits amid regulatory scrutiny and concern from privacy advocates and the advertising industry over the search giant’s approach to replacing the tool.

On Thursday, the Alphabet Inc. unit said its Chrome internet browser will stop supporting a user-tracking technology called third-party cookies by late 2023, nearly two years later than its initial time frame of early 2022. Google had announced the removal of cookies, which many companies in the advertising sector use to track individuals’ and target ads, under pressure from privacy regulators and advocates.

Google said the delay will give it more time to get publishers, the ad industry and regulators comfortable with the new technologies it is developing and testing to enable targeted ads in cookies’ wake.

“While there’s considerable progress with this initiative, it’s become clear that more time is needed across the ecosystem to get this right,” Google said.

The company’s plan to remove cookies is facing an array of regulatory scrutiny and complaints from privacy advocates who said it wasn’t going far enough to protect users’ data. Competitors said the search giant was using privacy concerns as a pretext to box them out of online advertising.

Earlier this week, the European Union said it is investigating Google’s plan to remove cookies as part of a wide-ranging inquiry into allegations that Google has abused its prominent role in advertising technology.

Google has separately pledged to give the U.K.’s competition watchdog at least 60 days’ notice before removing cookies to review and potentially impose changes to its plan, as part of an offer to settle a similar investigation. That probe stemmed from complaints that Chrome’s removal of cookies will give an advantage to ads on Google’s own products, such as YouTube or Search, where Google will still be able to do individual-level targeting.

The delay provides a reprieve for advertisers and ad agencies. Google plays a central role in the online advertising ecosystem. It owns some of the most widely used tools to broker the sale of ads across the web, and many of those ads appear via Chrome, the most extensively used web browser, with nearly 65% of the market globally, according to Statcounter.

Marketers are on edge over Google’s effort to retire cookies, ad executives said, and have rushed to find new ways to continue tracking and targeting their customers. Many have been working overtime to collect more first-party data about their customers through loyalty programs, newsletters, or creating direct-to-consumer businesses.

Google has been proposing and testing several new tools to replace various functions of third-party cookies without tracking people individually, as part of what it calls a Privacy Sandbox. The first such replacement technology, dubbed federated learning of cohorts, or Floc, is intended to allow advertisers to target aggregated cohorts of users with similar interests, rather than individuals, to protect their privacy.

But early technical testing of Floc, which began in April, has been slow. As early as January, in a press briefing and in talks with advertisers, Google suggested it would allow advertisers to test-buy ads for Floc in the second quarter. But it later indicated to several ad agencies and brands that their ability to test the new approach would begin in the third quarter, ad executives said.

Ad-industry players have also expressed skepticism about Google’s claims that Floc targeting is at least 95% as effective as cookie-based targeting. Several big advertisers said they want to be able to conduct side-by-side testing using cookies and Floc to compare.

Google engineer Michael Kleber said at a developer conference in May that the company is working out answers to how Floc should eventually work.

“We don’t have that ready yet because we don’t know what the answers are,” Mr. Kleber said. He added that everything “about how Floc works is very much subject to change.” The acronym Floc was chosen to reflect a flock of birds, he said.

Google said Thursday that it has “received substantial feedback from the web community” during the initial testing of Floc, called an origin trial. “We plan to conclude this origin trial in the coming weeks and incorporate input, before advancing to further ecosystem testing,” the company said.

It also said Thursday that it plans to complete testing of all of its new cookie-replacement technologies and integrate them into Chrome before late 2022. Then digital publishers and the digital advertising industry will have a nine-month period to migrate their services, during which time Google will monitor adoption and feedback. The final phaseout of cookies will happen over three months in late 2023, the company said, adding that it will publish a more detailed timeline.

Two rival web browsers that promote privacy, Mozilla’s Firefox and Brave, have said they aren’t supporting Floc. Some prominent websites have debated whether to opt out of using the system. The Electronic Frontier Foundation, a digital rights group, says Floc could be misused to help with device fingerprinting, a technique to identify specific web browsers without relying on cookies. That could potentially reveal sensitive information gleaned from web browsing, despite safeguards Google says it is building, the rights group says.

Some advertisers are concerned about those issues too. “Is Floc safe, or am I enabling or playing in this ecosystem that bad actors are also playing in?” one ad executive said.

On Thursday, Google said it is making progress in its work on technologies to hinder device fingerprinting via Chrome, including by reducing how much technical information a Chrome browser provides to websites it visits. A Google spokesman declined to comment further on the privacy concerns.

Google’s announcement comes just weeks after its rival Apple Inc. announced it would block users’ internet-protocol addresses in its Safari browser for the same reason.

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—Tripp Mickle contributed to this article.

Write to Patience Haggin at patience.haggin@wsj.com, Sam Schechner at sam.schechner@wsj.com and Suzanne Vranica at suzanne.vranica@wsj.com