The ASA said descriptions of speeds using the words "up to" is confusing and may be prohibited in changes to Committee of Advertising Practice rules next year.
Matt Hancock, the culture minister, tweeted that he was delighted by the move and that ads promoting broadband are "incredibly misleading".
The announcement comes two weeks after the ASA said that internet service advertisers must show all-inclusive up-front costs in their messaging and must no longer separate out line rental from their advertised charges.
Several ads have been banned by the ASA in 2016 for making "misleading claims", such as BT, whose high-profile ad starring actor Ryan Reynolds was censured by the watchdog.
Virgin Media has had two ads starring Usain Bolt banned by the ASA for misleading claims: one from 2015 in which Bolt appeared alongside characters called the Broadbandits, and one from the year before which claimed Virgin Media's service could download "five times faster than Sky and regular broadband".
In April, former culture minister Ed Vaizey described broadband ad rules as a "complete and utter joke".
Vaizey told the House of Commons culture, media and sport select committee, "The idea that if you can deliver to 10% of houses the broadband speeds you are advertising on a large billboard and get away with it seems to be a complete and utter joke."
Guy Parker, chief executive of the ASA, said: "Making sure ads don’t mislead is at the heart of what we do. We’ve taken action this year to tackle confusing broadband pricing, to the benefit of consumers.
"Our new research indicates that speed claims in ads contribute to consumers’ expectations of the broadband speeds they’ll receive, but their expectations are not being met. That needs to change."