The UK and Scottish governments have agreed to make it their long-term aim to have train journeys between London and Scotland's two main cities taking no longer than three hours.
Faster journeys than are currently possible will be enabled by High Speed 2, as the journey will take place on the faster tracks as far as Manchester and Leeds.
However, this will still mean journeys taking around three and a half hours to reach Glasgow and Edinburgh, so ministers of both administrations are to seek ways of making trips even faster.
HS2 minister Robert Goodwill said: "Together with the Scottish government, we will be asking Network Rail to identify any options with a strong business case, for consideration for inclusion in future plans."
The two governments also agreed to seek ways of reducing congestion on cross-border routes.
In its 2015 general election manifesto, the Scottish National Party called for HS2 to continue all the way up to Glasgow and Edinburgh.
