Robert Goodwill had been asked by a Labour MP about bringing the multi-billion pound rail to Edinburgh and Glasgow.
In reply he said: "I always think it is a good idea not to try to run before we can walk; let us get to Birmingham and Manchester first.
"I am sure that we will be looking at extensions, but they are not at the top of my to-do list at the moment."
His counterpart in the Scottish Government, Keith Brown, accused the minister of an attitude that was "not acceptable".
Mr Goodwill's transport colleague Baroness Kramer is due to announce the new study in Glasgow today.
The research is expected to look at how to cut journey times to Scotland to less than three hours.
Liberal Democrat Scottish Secretary Alistair Carmichael described the move as good news for Scotland, which could see significant economic benefits from the extension.
The Coalition Government is also understood to believe that taking the line to Scotland could help more towns and cities in northern England.
Ahead of her visit, Baroness Kramer said that the Coalition wanted to make HS2 a "truly national network that will bring the UK and its cities closer together".
The study will be carried out in co-operation with the Scottish Government.
Mr Brown said: "High speed rail has the potential to bring huge economic benefits to Scotland, but also adds Scotland's economic weight to the overall case for high speed rail across the UK.
"So we are willing to work in partnership with the UK Government to examine options for bringing high speed rail to Scotland, creating benefit for all and complementing the Glasgow-Edinburgh high-speed line which the Scottish Government is already planning."
Phase 1 of HS2, which will see trains travel to Birmingham by 2026, will cut journeys times between London and Glasgow or Edinburgh to around four hours.