The UK government Department of Transport has outlined the proposed route of the new transport system, which will run north of Birmingham to Manchester and Leeds.
However, Cllr Burns and Matheson called for an early announcement on plans to bring the network further north into Scotland.
Councillor Andrew Burns, Leader of the City of Edinburgh Council, said: "We welcome the announcement of Phase 2, which brings high speed infrastructure further north to Leeds and Manchester. It has already been demonstrated that the maximum economic and environmental benefits for the UK can only be realised if Scotland is part of the network.
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"This is why we are keen to see an early announcement on the next phase bringing this much needed rail infrastructure north of the Border and linking with the planned High Speed Link between Glasgow and Edinburgh."
Councillor Gordon Matheson, Leader of Glasgow City Council, said: "This is a welcome development because high speed rail will open up fantastic opportunities and growth for the UK.
"However, I have long argued that Scotland's two largest cities must be included in this network. It is essential that construction of a high speed rail route begins at both ends of the country and meets in the middle. If it doesn't then I believe our people and economy will be the losers - cut off from our major markets in England and Europe and at a huge economic disadvantage."
(IT)
