WASHINGTON — A government auction of airwaves for use in mobile broadband has blown through presale estimates, becoming the biggest auction in the Federal Communications Commission’s history and signaling that wireless companies expect demand for Internet access by smartphones to continue to soar.

And it’s not over yet.

Companies bid more than $34 billion as of Friday afternoon for six blocks of airwaves, totaling 65 megahertz of the electromagnetic spectrum, being sold by the F.C.C. That total is more than three times the $10.5 billion reserve price that the commission put on the sale, the first offering of previously unavailable airwaves in six years.

Prices are likely to rise further, because the auction has no definite end and could continue for days or weeks. The previous record was $18.9 billion raised in a 2008 sale of airwaves that, because of their lower frequency, are considered more attractive for wireless phone use than the current batch.

“It’s stunning,” said Preston Padden, executive director of the Expanding Opportunities for Broadcasters Coalition, a group representing broadcast television stations that are considering giving up their spectrum for sale in the F.C.C.’s next auction, scheduled for 2016. “Consumer demand for wireless broadband is on a growth curve that looks like a hockey stick, and carriers are desperate to keep up with that demand.”