The Scottish Government wants to press ahead between Glasgow and Edinburgh before the UK Government has committed to bring its High Speed 2 (HS2) project north of the border.
Deputy First Minister Nicola Sturgeon said the Scottish proposal would almost halve journey times between the two cities to less than 30 minutes by 2024.
The plan is at its earliest stage, with no costs attached or route map drawn.
It is also not known whether the link would be to existing or new stations, a spokeswoman said.
Launching the proposal in Glasgow today, Ms Sturgeon said: "We now know that, within just 12 years, we could build a line which will see journey times between our two major cities cut to less than half an hour.
"That will benefit our businesses, our jobs market and also our tourism industry, and it will put us up there with the world's greatest transport networks.
"We will not wait for Westminster to bring high-speed rail to us. We have already made moves towards seeing a high-speed line in Scotland and the evidence is now in place that this is feasible long before the HS2 proposals.
"The Scottish Government will now enter into talks with our partners in both cities and the rail industry to see how we can work together to see this vision realised: a Glasgow-Edinburgh high-speed line which can connect to the network from England."
The UK Department of Transport wants the first phase of its high-speed line to connect London and Birmingham by 2026, followed by extensions to Manchester and Leeds by 2033.
Scottish Transport Minister Keith Brown is expected to meet his UK counterpart, Patrick McLoughlin, for talks about linking Scotland in the coming weeks.
Glasgow City Council leader Gordon Matheson said: "I have long argued that bringing high-speed rail to both Glasgow and Edinburgh is vital for Scotland's economy.
"Today's announcement is therefore to be welcomed. Glasgow City Council is committed to working in partnership with the Scottish Government to bring high-speed rail to Scotland at the earliest opportunity."
Lesley Hinds, transport convener for the City of Edinburgh Council, said: "There is a very compelling case for bringing high-speed rail to Scotland, and the City of Edinburgh Council and our partners are united in our ambition of making this a reality at the earliest opportunity.
"The announcement of the potential for Edinburgh to be linked with Glasgow by high-speed rail by 2024 is a very welcome development towards this goal."
Network Rail boss David Simpson said: "I welcome the Scottish Government's continued commitment to supporting the development of Scotland's railway.
"We continue to work as part of Fast Track Scotland in developing plans for high-speed rail in Scotland and the exciting opportunities it would bring."
A two-day conference is under way in Glasgow, attended by politicians from Scotland and the North of England, as well as business leaders from London, to make the case for extending the HS2 line. Record producer and rail enthusiast Pete Waterman will address the event.
The Scottish Government says bringing the line to Glasgow could shorten the journey time to London by two hours and would generate £24.8 billion in the economy.
Mr Brown said: "This event will see many English local authorities join with us here in Scotland to show their support for a high-speed rail line which would benefit the whole of the UK.
"The Scottish Government looks forward to a future where Scotland stands on its own two feet as a nation, fully connected with its neighbouring communities.
"High-speed rail will play a huge part in that and sits squarely with this Government's two defining policy objectives: to increase the rate of Scotland's economic growth and to develop a low-carbon economy which leads the world in its ambition.
"Scotland is more than capable of taking the lead on innovation and partnership working, and local authorities north of London have already voiced their support for our proposals.
"This will offer an opportunity to see how we can work together to have all our voices heard.
"All local authorities which back the UK-wide line must surely see how that would positively impact on all areas along the way."
But Scottish Conservative transport spokesman Alex Johnstone criticised the lack of detail given to support the Glasgow-Edinburgh plan.
It would be just as easy to announce plans for a replica Taj Mahal built in the style of a Tunnock's Tea Cake, he said.
"In principle this kind of announcement should be welcome because cutting such journey times is important, but there is absolutely no detail given at all," said Mr Johnstone.
"The priority should be linking with the people we do most business with, and that is England, but the Scottish Government has stalled on this for years. Without costs and route plans, this is nothing other than pie in the sky nonsense.
"It would be just as easy for Nicola Sturgeon to announce plans for a Taj Mahal replica to be built, in the style of a Tunnock's Tea Cake, in honour of the First Minister."
Scottish Labour MSP Richard Baker said: "The Scottish Government is now committing itself to a rail upgrade when it doesn't even know how much it will cost.
"Long-suffering passengers will also remember that the SNP has axed the previously announced plans to dramatically reduce the travel time earlier this year.
"There is a trail of broken promises and letdowns for the passengers of our most-used rail line. Until the deal is signed and work begins, Scots shouldn't hold their breath.
"The SNP has a long list of delayed and costly mistakes on transport deals, from the Borders railway to road maintenance. It isn't surprising that we should all be a little sceptical of flashy announcements when the SNP can't get the basics right and commuters continue to suffer on their travels."