The Scottish government has said the rail link must be extended to Scotland
The UK government's proposals for a high-speed rail link must include extending the line to Scotland, according to Holyrood ministers.
UK Transport Secretary Lord Adonis has set out detailed proposals for the first stretch of the 250mph railway.
He said the first part of the route would run from London to Birmingham.
Under the proposals the high-speed trains would then continue on a y-shaped network stretching north to Glasgow and Edinburgh.
That would cut journey times between London and the two Scottish cities to three-and-a-half hours.
Scottish Transport Minister Stewart Stevenson said that extending the high-speed line to Scotland would make journey times of under three hours achievable.
It is understood that discussions between the Scottish government and the Department of Transport over how an extension north of the border would be funded are already under way.
Mr Stevenson said: "I am very clear that the business case for a high-speed rail link is greatly enhanced by bringing it all the way to Scotland and the transport secretary is very much of that mind too.
"The Scottish government has developed a compelling case for high-speed rail to Scotland, and it is vital that it happens.
"Scotland's transport future must include high-speed rail, and we will work with the UK government to help deliver it."
Lord Adonis said the London to Birmingham link would cost between £15.8bn and £17.4bn, with work due to start in 2017.
Secretary of State for Scotland Jim Murphy said: "I think there will be a strong business case for extending high speed lines to Scotland.
"The decision on creating those lines in Scotland is devolved but I know many Scots would welcome a Scottish government decision to match the UK's ambition for our rail network."
Shadow Secretary of State for Transport Theresa Villiers MP has said: "The Conservatives are committed to taking the second phase of high speed rail to Scotland.
"As Labour conceded earlier this week they haven't even initiated a dialogue with the SNP government about funding for it.
"In contrast, the Conservatives held a productive meeting with John Swinney over a year ago."
Scottish Liberal Democrat transport spokeswoman Alison McInnes MSP said: "A high speed rail link to the capital won't help businesses in the north of the country.
"High-speed rail promises to cover the 330-plus miles between our two capitals in less than three hours.
"But travellers and commuters wanting to travel on to the capital of the Highlands, Inverness, face another three hour journey to cover just 120 miles. That's the same journey time for half the distance.
"The Scottish transport minister needs to make sure that high-speed rail from London is met in Scotland by a much improved Scottish train system, which gets people all around the country quickly. The SNP must not duck their own rail responsibilities."
Liz Cameron, chief executive of Scottish Chambers of Commerce, said: "Scotland must be a part of our national high speed rail network from the outset, and this announcement does not go far enough for Scottish businesses.
"Independent research has estimated the economic benefits of HSR to Scotland to be in excess of £7bn, and there are significant environmental and productivity benefits to be gained from the modal shift from air to rail that such an investment would bring to Scotland".
Dr John McCormick, chairman of the Scottish Association for Public Transport, said: "The first French high-speed TGV line opened more than 25 years ago.
"While Britain is over 25 years behind in developing high-speed rail, it is important that a sensible Anglo-Scottish route gets cross-party political support, both at Westminster and Holyrood, as this project will inevitably take decades to complete".
Friends of the Earth Scotland's head of campaigns, Juliet Swann, said: "Suggesting a high-speed rail link from London that ends in Birmingham is like swapping a horse for a donkey mid journey.
"An essential component in making climate friendly choices open to all is investing in a high-speed rail link between Aberdeen and London."
She added: "This half-hearted effort shows a lack of ambition and is profoundly short-sighted."