The disagreement could affect whether states join a Justice Department complaint about Google. Like the states, federal antitrust enforcers have been investigating whether Google is thwarting competition in the digital advertising market, where it holds a commanding position.

The Justice Department, which is coordinating with the states, wants to move quickly, two of the people said, and is on track to file a complaint this summer, another person said, though it wasn’t clear what conduct the complaint will ultimately target. The department declined to comment.

“While we continue to engage with ongoing investigations, our focus is on creating free products that lower costs for small businesses and help Americans every day,” Google said in a statement.

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State attorneys general can play a pivotal role in enforcement cases against companies when they band together in group investigations. They joined the Justice Department in suing Microsoft Corp. in 1998 for antitrust violations. The case nearly led to the break-up of the company when a judge sided with the government. After an appeals court reversed the ruling, the Justice Department under the George W. Bush administration settled the case.

Two people familiar with the states’ investigation said the split among the states reflects normal tension about the best litigation strategy. A broad complaint would cover more conduct but would take more time to complete.

Texas Attorney General Ken Paxton is leading the investigation into Google’s conduct in the digital advertising market, which was announced in September on the steps of the Supreme Court. Other states, including Utah and Iowa, are focusing on internet search. Google dominates web search in the U.S., and rivals have complained that the company has prioritized its own services, such as travel and restaurant reviews, in results.

Texas declined to comment. Representatives from Utah and Iowa didn’t immediately respond to requests for comment.

The digital advertising part of the probe focuses on Google’s control of the tools that deliver display ads across the web. Google owns much of the technology used by publishers and advertisers to buy and sell advertising space. Google has been accused of using its dominance to siphon advertising dollars from publishers.

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Texas is in the later stages of its probe in advertising and could join the Justice Department’s case with some states, said two of the people. States are still waiting to get a full look into the federal complaint, one of the people said.

The investigations are so complex that few among the enforcers have a sense of what the Justice Department and all the states are doing, two of the people said.

The investigation into online search is not advanced as far as Texas’s probe into the digital ad market, and some states are pushing for more time to investigate, said the people. At one point, states were also looking the company’s mobile operating system, Bloomberg reported last year, though it wasn’t clear whether that is an active part of the investigation.

The chief executive officer of Google search rival DuckDuckGo Inc. said last month that state and federal enforcers have asked detailed questions about how to limit Google’s power in the search market as recently as the spring.