The MPs called for a "step-change" in efforts to tackle the growing problem, with measures to improve enforcement, raise awareness and develop technology to stop unwanted sales calls.
The All-Party Parliamentary Group on Nuisance Calls said industry regulator Ofcom should do more to help vulnerable customers who could find themselves on a "suckers list" used by people running scams.
The report found that "current trends indicate nuisance calls and texts are on the increase" and "there is the looming threat of nuisance calls being made to mobile phones" as costs drop.
"The group concludes that the current situation is untenable: constituents are not well-served by the existing regulatory structure nor by the wide spread of shared but weak responsibility, which has ultimately resulted in no one taking overall control."
The MPs added: "The continued growth of nuisance calls suggests that a step-change is needed. We require a specific, targeted push across several fronts - enforcement, awareness and technological solutions - to begin to reduce nuisance calls and limit consumer detriment and distress."
The MPs recommended that telecoms companies block numbers known to be making nuisance calls.