Ministers may consider moves to ban young drivers in England and Wales from carrying anyone except family members as passengers, reports suggest.
Transport Secretary Patrick McLoughlin told the Daily Telegraph he was looking at ways of reducing road deaths involving newly-qualified motorists.
Insurers believe peer pressure on young drivers can lead them to take risks.
The Department for Transport says the issue is being considered but there are "no plans" for legislation.
The Association of British Insurers says drivers aged 17-24 are responsible for a disproportionately high number of crashes, deaths and claims.
It says an 18-year-old is more than three times as likely as a 48-year-old to be involved in a crash, and that a third of drivers killed in car accidents were under 25.
That was despite the fact that the under 25s form only one in eight of all car drivers.
In an interview with the Daily Telegraph, Mr McLoughlin said he would consider measures put forward by the ABI which could cut the number of accidents involving young motorists.
"I read regular reports where three or four young people have been killed in a car, and it's a new driver, and you wonder what happened," he told the newspaper.
"When I talk to young people who have recently passed their test, what they say sometimes is that peer pressure is put on them to go fast, to show off.
"They are not anticipating an accident, but something goes wrong. They are not drivers with a huge amount of experience by the very fact of their being new drivers. I think we have got to look at that.
"There is a suggestion as to whether you should look at a restriction whether anyone could carry passengers for six or nine months when they have first passed their test.
"There are suggestions about them only perhaps being allowed to take a family member to drive a car when you are learning, you have to have a qualified driver in the car. So these are all sorts of areas that I think we can look at."
It comes six weeks after the Association of British Insurers called for an overhaul in the system - suggesting people should spend a year learning to drive and urging the introduction of a graduated licence for the first six months after passing a test.
ABI spokesman Malcolm Tarling denied that a restriction on who young drivers could carry as passengers would be difficult to enforce.
He said: "In terms of policing, you could use that argument for just about anything, really.
"Other countries have adopted these measures and their experience has shown that they're largely self-policing.
"Of course there will always be people who will look to avoid the law, but the reality is if you impose something like this, and encourage people to follow it, international experience has shown that that is exactly what people do."
But Neil Greig from the Institute of Advanced Motorists said forcing young motorists to carry only family members with them in the car would not necessarily make them safer drivers.
"Young drivers themselves admit that they are lacking experience, but we don't believe that restricting people - such as curfews at night and restricting the number of passengers they can carry - is the way to develop that experience.
"They need the opportunities to get to learn, by doing these things, by carrying young people, by going out at night - how else can they learn?"
A Department for Transport spokesman said: "Improving the safety and ability of young drivers is a key priority for the government, which is why we have made the driving test more realistic - and are also considering how to improve training for drivers after they pass their test.
"There are no plans to introduce graduated licensing in England and Wales.
"However, we are working with young people, the insurance industry, and other key partners to identify what more can be done to ensure that newly qualified drivers are properly prepared and drive safely.
"We will consider carefully any ideas that reduce the risks of accidents involving young drivers."