It has been claimed the move would save the taxpayer £100 million a year and enhance customer experience on the railways by reducing journey times and delays.
Any savings would also be reinvested to fund increased services and improved rolling stock.
Scottish ministers are already responsible for the funding and managing of railways north of the Border through the ScotRail franchise which is currently operated by Dutch company Abellio.
However, Network Rail - which is responsible for managing the track, signalling and infrastructure - answers to the UK Government, even though its performance has a direct impact on ScotRail.
Transport Minister Humza Yousaf will urge the leaders of other political parties to support the push for Network Rail to be accountable to Holyrood.
The call will come as figures show that, over the past year, 54 per cent of delays over three minutes were due to Network Rail faults on the line.
This compares to 37 per cent which can be attributed to ScotRail.
Reform Scotland made the same call last November but UK transport secretary Chris Grayling refused calls for more control to be handed to Scotland.
In a letter ahead of a committee to discuss the performance of the railway, Mr Yousaf asked rival parties to support the devolution of powers over Scotland’s railway.
His letter says: “Decisions around a number of basic functions critical to the success of our railway are taken outside Scotland at a cost in excess of £100m a year.
“The Scottish Government is of the view that functions such as capacity planning, major projects delivery, timetabling, legal and property management pertaining to Scotland could and should be devolved and in so doing would provide improved responsibility, accountability, operational efficiency and better alignment with Scotland’s needs and priorities.
“I’m sure you agree the current arrangements fall short of what is required and would welcome [your] support [for] the Scottish Government’s efforts to secure the full devolution of Network Rail and thereby help ensure that the rail industry in Scotland is better placed to deliver the best possible outcomes for passengers.”
One industry source said: “Of course there are political complaints about the railways. Parties wouldn’t be doing their job of opposing if they weren’t.
“But they want the head of a minister for stuff he’s not accountable for. We have it pretty good with the railways in Scotland. Westminster isn’t keen on this plan because they are playing catch-up with much worse performance figures.”
Network Rail said the ScotRail Alliance “already provides a dedicated and devolved rail network to Scotland”.