The Federal Communications Commission dismissed yesterday a request by the company providing cable television service in Fairfax County to scrap more than $10 million in obligations it promised the county during contract negotiations three years ago.

The FCC declined to rule on the merits of the petition by Media General Cable of Fairfax Inc., saying in effect that it had no power to consider it. Media General had argued that the costs of a wide range of services, including wiring public schools and a commercial network information system, should be subtracted from the annual franchise fee it pays to the county because those services do not benefit all subscribers.

Media General could now seek relief through court action, either against the FCC or against Fairfax County, according to FCC officials.

"I'm pleased that the FCC dismissed the petition, which is what we thought was the proper disposition of the case," said Mike Long, an assistant county attorney in Fairfax.

"I expected this is the turn it might take," said Thomas E. Waldrop, executive officer and chairman of the board of Media General. He declined to specify what action the firm might take now.

Media General said its petition to the FCC, filed in March, was an attempt to clarify new guidelines approved by Congress last October. The guidelines limit the type of extra services localities can require cable companies to provide.

But county officials have spoken angrily about the Media General petition, charging that the firm was trying to get out of its promises to the county.

Waldrop disagreed. "It was never our intent to welsh on anything," he said.