According to the regulator, 70% of the complaints it receives are from consumers who receive two or more silent calls every day, for a number of days or weeks, from the same company.
It believes these repeat calls are caused by imperfect answer machine detection (AMD) technology, which is designed to hang up when outbound calls go through to an answer machine.
In some cases, the AMD technology mistakes a live person answering the phone for an answer machine, leading to the person hearing silence on the line.
Ofcom has therefore proposed a new rule, barring companies from calling a supposed answering machine more than once in 24 hours, unless a call centre agent is on hand to take the call.
Ofcom said that this measure would mean those consumers "worst affected would no longer receive repeat silent calls over the course of a day".
The new rules are set to come into effect from early next year
The regulator added that if it continued to receive high volumes of complaints about silent calls, it would ban AMD systems outright, or insist that the industry adopt a 100% accurate AMD system.
Ed Richards, Ofcom's chief executive said: "Silent and abandoned calls can be very irritating and even frightening for some people.
"By tackling repeat silent calls, backed by firm enforcement action, Ofcom expects to see a sharp reduction in consumer harm."