Google declined to comment for this article.

Google’s search engine makes tens of billions of dollars in advertising revenue annually and has outsize power to influence what people see online — competitors complain regularly. But in the recent Android case, Google’s opponents made a strategic decision by going to the Justice Department first.

Both the Justice Department and the F.T.C. can open antitrust investigations, and they have gone back and forth on a number of Google inquiries.

Still, in 2013, Internet companies including Microsoft and Yelp were incensed when the F.T.C. — after a long investigation into whether Google used its search engine to unfairly favor its own products — unanimously voted not to bring antitrust charges. At the time, critics complained that the F.T.C. investigated the wrong things and that its decision not to bring a case rested heavily on Google’s own logic.

Those cries grew louder this year when the F.T.C. inadvertently sent The Wall Street Journal part of a 2012 report from its agency of competition. In the report, staff members said the F.T.C. should sue Google for some of its anticompetitive practices and raised concerns about how the company ranked competitors in its search engine.

A few months ago, according to the two people involved in the investigation, the Justice Department asked the F.T.C. for clearance to investigate the recent Android complaints — in essence, it asked the F.T.C. for authorization to start making calls and taking meetings with Google’s opponents. Ultimately, the Justice Department and the F.T.C. worked out an agreement for the F.T.C. to take up the issue instead.

A spokesman for the Justice Department declined to comment for this article.

The resulting inquiry is in a fact-finding stage, and the F.T.C. has yet to contact Google, according to the people involved in the inquiry. However, the F.T.C. agreement with the Justice Department suggests that the inquiry has accelerated and that the F.T.C. is at least willing to dedicate staff members to the issue.

“We welcome an investigation,” said Matt Reilly, legal counsel at FairSearch, a group of several Google competitors, including Microsoft. FairSearch has initiated antitrust cases against Google in the United States and in Europe. “Once they dig into the evidence, we expect it will be clear that Google’s Android practices harm innovation and consumer choice.”