A Google was targeted Thursday in an antitrust lawsuit joined by 38 states, which alleged that theAlphabet Inc. GOOG -1.02% unit maintained monopoly power over the internet-search market through anticompetitive contracts and conduct.

The states alleged that Google leverages its position as the dominant search engine—and the personal data such a perch allows the company to gather—to limit consumers from using competing search engines, force businesses to use its proprietary advertising tools and foreclose competition from specialized search engines for travel or local businesses.

“Consumers have better products and services when they’ve got choice in the marketplace, and they’ve been deprived,” said Democratic Colorado Attorney General Phil Weiser at a video-streamed news conference with other state attorneys general.

“This will be a unified effort,” said Iowa Attorney General Tom Miller, a Democrat.

Google has long said it operates in a competitive market.

In a blog post Thursday, Google economic policy director Adam Cohen said some of the actions described in the suit were taken to improve search results.

“We show information that helps you connect with businesses directly and helps them reach more customers,” Mr. Cohen wrote.

“This lawsuit demands changes to the design of Google Search, requiring us to prominently feature online middlemen in place of direct connections to businesses.”

The 38 states filed in U.S. District Court in Washington, D.C., the same venue where the Justice Department filed a suit Oct. 20 against Google targeting its search business.

Mr. Weiser said they were seeking to join the two lawsuits into one piece of litigation.

Another state case, which focused on Google’s digital advertising empire, was filed Wednesday in a Texas federal court.

Thursday’s suit asks the court to order actions that prevent Google from harming competition, “including but not limited to structural divestitures.” The states didn’t specify what divestitures they might seek.

Google has called the federal suit and the Texas-led suit deeply flawed, arguing that it competes on merit and maintains dominance because consumers choose its product first.

Thursday’s suit added allegations not covered in detail in the other two lawsuits, echoing concerns long voiced by specialized digital information providers such as Yelp Inc. and Tripadvisor Inc. TRIP -1.33% that Google has discriminated against them to curtail their growth.

Both those companies applauded the move.

One allegation focuses on SA360, a Google-owned tool for placing ads on internet searches. Google promised advertisers they could use the tool to place ads on the Google search engine as well as others, such as Microsoft Corp.’s MSFT -0.73% Bing, but actually designed the tool to lend an advantage its own search engine, according to the suit.

In response, Google executives told reporters on a Thursday conference call that the company isn’t obligated to help advertisers to place ads with the competition.

The suit also accuses Google of seeking to forestall competition from rivals that could siphon search traffic and revenue using new technologies or specialized services.

It cites contractual requirements and other actions that, according to the suit, are designed to ensure mobile phones, voice assistants, connected cars and other technologies use Google search.

The Google executives said these markets are highly competitive.

It also cites the way Google designs search results. It alleges that when consumers search for an electrician ora hotel, Google displays advertisements and other results in a way that favors Google-owned travel or recommendation services, rather than those provided by other companies.

In the blog post, Google’s Mr. Cohen noted that some of the claims about search bias were reviewed by the FTC during the Obama administration—and the FTC decided not to bring a suit.

The states’ suit also repeats some allegations made in the Justice Department case, such as an accusation that Google foreclosed competition through a deal with Apple Inc. AAPL -0.77% to make Google the default search engine on i Phones.

For now, the suit filed in Texas covers different terrain than the two Washington, D.C.-based actions.

It accuses Google of abusing its power over the complex, highly technical market for displaying ads across the web.

Some of those claims could later be added to the other lawsuits filed in Washington.

The Justice Department has been posing detailed questions to Google’s rivals about that part of Google’s business, according to people familiar with that probe.

The separately filed suits partly reflect a practical division of labor.

Agencies with limited resources divvied up the work of probing different aspects of Google’s business.