SAN FRANCISCO, July 31 — The Federal Communications Commission moved cautiously Tuesday toward creating a more open national wireless broadband network, handing a partial victory to Google, which was pushing for more competition in cellphone services.

The agency approved rules for an auction of broadcast spectrum that its chairman, Kevin J. Martin, said would promote new consumer services. The rules will let customers use any phone and software they want on networks using about one-third of the spectrum to be auctioned.

The F.C.C. did not approve a provision that would have required the winner of the auction to sell access to its network on a wholesale basis to other companies. Google favored the rule as a way to hasten competition and innovation in the cellphone industry, a market it is considering.

While the language of the ruling has not been made public, it appears that any company that buys the new spectrum will have to leave it open to devices it does not approve or control. If, for instance, Verizon were to buy spectrum, consumers would have to pay Verizon for access to its network but they could use devices of their own choosing on it.