A study aiming to increase the benefits to Scotland of the HS2 rail project has been announced by the UK government.
The work by HS2 Ltd suggests high-speed services to Scotland and the north of England will start as soon as Phase One opens in 2026.
UK transport minister Baroness Kramer said the project would "bring the UK together".
Scottish Transport Minister Keith Brown said he was "excited" to work with the UK government on the plan.
Phase One will consist of a new high speed rail line between London and the West Midlands, with a completion date of 2026.
When Phase Two is completed in 2032/33, lines will run to Manchester and Leeds, the government has said.
In June the government revised the estimated cost of building the high-speed link between London and the North of England from £32.7bn to £42.6bn.
Phase one will see journey times between London and Glasgow/Edinburgh reduced from four hours 48 minutes to four hours, while these times will fall further to three hours 38 minutes when the phase two is up and running.
The UK government, which has been holding talks with Transport Scotland, has instructed HS2 Ltd to look at further rail capacity and journey time improvements for northern England and Scotland.
This is to include the possibility of eventual journey times from Glasgow and Edinburgh to London of three hours or less.
Baroness Kramer told BBC Radio's Good Morning Scotland programme: "Scotland has always been part of the picture from day one of the high-speed project and will benefit from day one as soon as the first phase of it opens.
"What we have always said is 'look, we can do more' and the study I have come up here to launch is to do exactly that."
She added: "Scotland will already be getting £3bn in economic benefit and shorter journey times but we want to get under that three-hour benchmark and also look at other ways we can use to support the Scottish economy."
Scotland's transport minister said: "The Scottish government's position is that high-speed rail should come to Scotland.
"I have said that to three different UK transport ministers," Mr Brown said.
He said getting the journey times down below three hours would result in a "modal shift", meaning that people would consider rail as an option instead of road or air.
"That's why the Scottish case for high-speed rail helps the UK case for high-speed rail," Mr Brown said.
He called on the UK government's Scottish Secretary Alistair Carmichael to "unequivocally" back Scotland's inclusion in the HS2 network.
He added: "You don't have to start this line in London and go north. Given the fact you don't have the same opposition in Scotland that you do in parts of England we could make a very quick start in Scotland."
Emma Crane, the Scotland campaign manager of the HS2 Action Alliance, told Good Morning Scotland: "It is very important for the Westminster government for Scotland to approve of this project. But if you have a look at the facts and the benefits for Scotland, they don't really stack up at all.
"92% of all rail journeys in Scotland begin and end in Scotland. There is very little cross-border travel so anything like this is not going to benefit a large proportion of the Scottish population."
She added: "It is a London-centric policy which is going to cost Scotland a huge amount of money."