Current laws give the “misleading impression” that hands-free options are safe, they warned.
While it has been illegal to use a handheld phone at the wheel since 2003, using a hands-free device creates “the same risks of collision”, the Commons Transport Select Committee said.
The government said that, where legal, drivers must always use phones safely.
An expert told the committee that taking a hands-free phone call caused “essentially the same” amount of distraction as being at the legal limit for alcohol blood level in England and Wales.
A public consultation on the proposal should be published by the end of 2019, the cross-party group said.
It would only apply to England and Wales, as the issue is devolved in Scotland.
‘Lifetime of suffering’
Joshua Harris, of road safety charity Brake, said research showed using a hands-free phone “can impair a driver in the same way as a hand-held device and so it makes sense that the law treats these acts equally”.
“One moment’s distraction from a phone can cause a lifetime of suffering so our advice to drivers is simple – when you’re driving, make sure your phone is on silent and placed out of sight and out of reach,” he said.
There were 773 casualties on Britain’s roads in 2017, including 43 deaths and 135 serious injuries, in crashes where a driver using any kind of mobile was a contributory factor, the committee said in a report.
While the number of people killed or seriously injured in such incidents has increased since 2011, the rate of enforcement regarding phone use has fallen by more than two-thirds over the same period, the report added.
Since March 2017, motorists caught using a handheld phone have faced incurring six points on their licence and a £200 fine – up from the previous penalty of three points and £100.
The MPs urged the government to consider whether penalties should be increased further “to better reflect the serious risks created by drivers committing this offence”.
Labour MP Lilian Greenwood, who chairs the committee, said “any use of a phone distracts from a driver’s ability to pay full attention” to the road.
A 2016 study by scientists at the University of Sussex found conversations via hands-free devices caused some drivers to visually imagine what was being discussed.
A Department for Transport spokeswoman said: “While mobile phones are a vital part of modern life and business, drivers must always use them safely and responsibly.
“Being distracted by a mobile phone while driving is dangerous and puts people’s lives at risk. The law is clear that anyone driving dangerously is committing a criminal offence.”