Transport Secretary Patrick McLoughlin has said he "wants to look at" doubling the penalty for using a mobile phone while driving.
The head of the Metropolitan Police, Sir Bernard Hogan-Howe, has called for the punishment to be upped from three points on a driving licence to six, meaning a driver would be banned if caught twice in the space of three years.
Speaking at a lunch with journalists, Mr McLoughlin said he was considering the step in an effort to lower the "appalling" number of accidents involving drivers using mobiles.
"Sir Bernard Hogan-Howe has called for six penalty points for the use of a mobile phone. It is an interesting suggestion, " he said.
"It is one that I would want to look at. There could be some difficulties about it but I think we have got to get the message across to people about safety.