WASHINGTON – U.S. regulators ended discussions with companies on Internet regulation after the closed-door talks drew criticism and Google Inc. and Verizon Communications Inc. were said to have reached their own deal.

The talks, begun in June, haven’t “generated a robust framework to preserve the openness and freedom of the Internet,” Edward Lazarus, chief of staff of the Federal Communications Commission, said Thursday in a statement.

At issue was the FCC’s power over providers of Internet service and whether phone and cable companies may favor some Web traffic, such as speeding certain videos in return for payment. Among participants were AT&T Inc., Verizon, Google, Skype Technologies SA, and the National Cable & Telecommunications Association, representing companies led by Comcast Corp. and Time Warner Cable Inc.

“We’re relieved to see that the FCC now apparently finds dangerous side deals from companies like Verizon and Google to be distasteful and unproductive,” Derek Turner, research director of the Washington-based advocacy group Free Press, said in an e-mailed statement. “The corporate deal-making and the closed-door meetings have generated widespread public outrage.”

Verizon, the second-biggest U.S. phone company, and Google, owner of the largest Internet search engine, reached their own agreement on network rules as the federal talks were under way, two people briefed on the discussions said Wednesday.

The compromise would restrict Verizon from selectively slowing Internet content that travels over its wires, but wouldn’t apply such limits to Internet use on mobile phones, according to the people, who asked not to be identified before an announcement.

FCC Chairman Julius Genachowski told reporters Thursday that any resolution “that doesn’t preserve the freedom and openness of the Internet for consumers and entrepreneurs will be unacceptable.”

The long-running fight over net neutrality has pitted cable and phone companies that say they need leeway to protect the performance of their networks against content providers and advocacy groups that say the communications companies may favor their own online offerings or those of partners.

The negotiations at the FCC, led by Lazarus, followed a court decision in April that eviscerated the agency’s authority over Internet service providers, and Genachowski’s subsequent proposal to claim authority using rules applied to phone calls. His idea sparked opposition from phone and cable companies and from members of Congress from both parties.

AT&T, the biggest U.S. phone company, is disappointed the FCC talks broke down, Jim Cicconi, senior executive vice president, said in an e-mail.

“We put a number of significant concessions on the table and, despite today’s setback, remain convinced that a consensus solution can be achieved,” Cicconi said.

The FCC should claim authority over Web service providers and pass rules ensuring an open Internet, following the “collapse” of the talks, Gigi Sohn, president of Public Knowledge, a Washington-based advocacy group, said in an e-mail.