He said the Scottish Government is still talking with the UK Government about bringing the line further north.
This week the UK Transport Secretary Patrick McLoughlin announced extending the route for High Speed 2 (HS2) from London to Birmingham on to Manchester and Leeds.
The Scottish Government said it was planning for a high-speed line between Glasgow and Edinburgh regardless and wants to see it linked with a line coming north from England.
Mr Brown said Mr McLoughlin's announcement on the proposed extension was supported by analysis that £3 billion economic benefit would come to Scotland once that line is complete in 2033.
He said: "However, our ambition is for full high-speed connections linking both Glasgow and Edinburgh with London and other cities across the UK.
"Our analysis is that a full network would deliver economic benefits of £24bn to Scotland."
However, Kenneth Gibson, Cunninghame North SNP MSP, said the construction costs for Scotland would top £3bn.
He said the UK Government was "adding insult to injury", and asked the minister if he would be seeking additional resources from Westminster to enhance the Scottish rail network.
Journey times from the north of England to London would be halved, while reduced by only 12% from Glasgow and Edinburgh.
Mr Brown said he would rather see a commitment from the UK Government to bring high-speed rail further north, but would be interested to see what benefit Scotland receives from the amount being spent south of the border.
He added: "I don't believe the door is closed on that. We have had some positive comments from the Prime P7inister and the secretary of state.
"We will continue to push the UK Government as we believe we can work with them to make sure we have those benefits. That would be the best way to spend the money.
"We have shown we will push ahead with a high-speed rail link between Edinburgh and Glasgow.
"We want the UK Government to come with us so we can deliver a high-speed rail network that will deliver benefits to the whole of the UK."