More than two-thirds (69%) of fleets questioned in the RAC's report, 'Driving on Company Business' say they would drive up safety standards if they were liable to prosecution.
They are also supportive of a limit on the number of hours fleet motorists can drive per day, with 77% giving the idea their backing.
However, only 42% of firms agreed with a proposal to make company car drivers automatically liable for any accident unless they had proof that they had undergone additional training to prepare them for business driving.
Just over one-third of fleets back the use of monitoring and telematics to improve safety, while 32% support compulsory 'Well Driven?'-type labels.
Mandatory company logos and telephone numbers on cars are supported by 29%, while 22% gave their support to additional exams for business drivers before they could get behind the wheel.
Simon Cashmore, managing director, corporate services at RAC Motoring Services, said: 'At the heart of our research lies the question of how seriously fleet decision-makers need to take their corporate responsibility.'