Transport Minister Keith Brown appealed to Boris Johnson and newly-elected council chiefs in northern England a day after polls were held across the UK.
Mr Brown wrote to 54 local authorities, urging them to attend a meeting to discuss the benefits of a UK-wide network, estimated to cut as much as two hours from journeys between Glasgow and London.
The line is due to link London and Birmingham in its first phase.
Mr Brown said: “There is no better way for these new council leaders to prove they are progressive and working for the future of their local areas than 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.
“I have issued this invitation to show that Scotland is more than capable of taking the lead on innovation and partnership working, and because most local authorities north of London have already voiced their support for our proposals.
“I would hope that Mr Johnson will also see how London can only realise the full potential of high-speed rail when it connects all the way to Scotland.”