The demand comes amid growing question marks over the SNP's handling of the ScotRail crisis.
The party is issuing 10 key questions to the Scottish Government today over its "half-baked" proposals for rail nationalisation - set out for the first time in a TV studio on Sunday.
The Scottish Conservatives have also warned that any plan to renationalise the ScotRail contract may not be possible until 2022 - six years away - offering scant hopes to passengers suffering lengthy delays.
Mr Yousaf must now come before the Scottish Parliament, shadow finance secretary Murdo Fraser said, or at least give evidence to a Holyrood committee setting out in detail how his new plans will work.
Scottish Conservative shadow finance secretary Murdo Fraser said:
“It's clear that Humza Yousaf's half-baked plan for rail nationalisation was cooked up in a TV studio in order to deflect attention away from his handling of the ScotRail contract.
“He is throwing a bone to the rail unions who have demanded his resignation.
“If this is a serious proposal, he needs to offer some clear answers to parliament on how exactly it would work.
“How much would it cost taxpayers? Who would pay for new trains? Either Mr Yousaf can answer these questions, or we will know for sure his plans were scribbled over the weekend on the back of a fag packet.
“Mr Yousaf also needs to come clean and acknowledge that it could be six years before a public sector contract could begin. That is no help to passengers waiting on delayed trains who want action now.
“The SNP's transport minister is trying to spin his way out of a crisis. He needs to come before parliament and set out exactly what he is planning - and why it will be of benefit to passengers and taxpayers."
The ten questions for Mr Yousaf are:
1. What is the earliest date that the Scottish Government envisages a public sector operator taking over the ScotRail contract?
2. What costs would be incurred in setting up a public sector rail operator?
3. What would be the running costs of a new public sector agency changed with managing the contract?
4. What level of expertise exists within the public sector to run the rail system in Scotland?
5. Does the Scottish Government envisage a public sector contract run by an arms-length body, or from within the Scottish Government core departments?
6. Has the SNP carried out a risk assessment of the potential cost to taxpayers if the network is renationalised?
7. Are there penalty clauses that will have to be paid if the contract is taken out of the private sector and handed to the public sector?
8. What access to capital would the public sector have in order to replace older trains with new rolling stock?
9. What impact on reliability do the Scottish Government expect/What proportion of train reliability can be directly attributed to ScotRail’s operation and would be improved by a public sector operator?
10. Given the Scottish Government’s inability to manage a contract, what specific mechanisms would be put in place to directly manage a service?
