The SNP, backed by Labour MSPs, wants to see a range of measures brought in that would put limitations on drivers under the age of 25.
Statistics, which show that younger drivers are more likely to be involved in accidents and more likely to be killed, have led to calls for action.
Keith Brown, Transport Minister, said 17 to 25-years-olds make up 10% of the driving population but account for 23% of accidents.
He wants the UK Government to either take action and implement a graduated driver licensing programme or devolve power to Holyrood to allow the Scottish Government to do so.
The measures, adopted in other countries including the USA, Sweden, Australia and proposals drawn up for Northern Ireland, include a mix of different measures.
It could include a ban on night time driving, a lower drink drive limit, restrictions on carrying passengers or a limit on the car's engine size.
Mr Brown said: "I have written several letters to the UK Government urging it to take action or give powers to the Scottish Parliament. Research shows 19 lives per year could be saved in Scotland."
"Graduated licensing remains the only intervention which shows a reduction in accidents involving young drivers."
He said young drivers were more at risk of an accident at night and when other young people where in the car, with a fifth of accidents occurring between 9pm and 6am.
Labour backed the plans while the Conservatives said there were different considerations in different parts of the country.
Mark Griffin, Labour's transport spokesman said the Scottish Government also needed to come forward with some proposals and suggested a rehabilitation programme for young drivers who are serving prison terms.
However, he said Labour backed the proposals and added: "The statistics speak for themselves. Road accidents are the biggest threat to young people."
Alex Johnstone, for the Tories, said road policing had to change and said in rural areas curfews wouldn't work and suggested allowing people to take lessons at 16, but still unable to take a test until 17.
He said he came from a rural background where people started to learn to drive "as soon as their feet reached the pedals".
He said: "I am concerned by the idea legislation can improve safety. The behaviour which leads to these terrible accidents we all want to stop is already outside the law."