States are turning up the pressure on federal regulators to police the biggest tech companies and give consumers more control over their personal data.

Attorneys general in several states have already opened or are preparing investigations into Facebook, Apple and Google over concerns about privacy and anti-competitive practices. They lobbied the Justice Department to take action last fall, and on Wednesday, they are meeting with the Federal Trade Commission in Nebraska to discuss antitrust enforcement.

In a letter to the agency sent Tuesday night, the AGs called for tougher reporting requirements for tech acquisitions and a new clearinghouse for data brokers. The letter was signed by 39 states, along with the District of Columbia, Guam and Puerto Rico.

"Each one of those companies, individually, needs to be looked at and overlaid against our consumer protection and antitrust laws to determine whether or not the activity each one is engaged in would render a breakup or not," Louisiana Attorney General Jeff Landry, who heads the National Association of Attorneys General, told CNBC. "Whenever nascent industries come about, and they gain economic power and they gain monopolistic control over that market, we've seen our government come in and break those particular companies up."

Washington is starting to take notice. The House Judiciary Committee kicked off a broad investigation into the dominance of the tech giants this week. Federal regulators have open inquiries into Facebook, Google, Apple and Amazon, according to a person familiar with the probes. And the Justice Department's top antitrust official is pushing back against criticism that the agency has been slow to respond to a rapidly changing industry.

"The antitrust division will not shrink from the critical work of investigating and challenging anticompetitive conduct and transactions where justified," Assistant Attorney General Makan Delrahim said in a speech Tuesday in Israel.