The SNP's Fiona Hyslop and Conservative Adam Tomkins went head-to-head in a TV debate which looked at Brexit and a possible second Scottish referendum.
They took questions from an audience gathered at BBC Scotland's headquarters in Glasgow.
The Reporting Scotland special came at the end of the first day of a two-day Holyrood debate on requesting a fresh referendum.
The SNP government wants a second vote, the UK Tory government said "not now".
Ms Hyslop said that Brexit had "changed everything" and that was why an independence referendum bid was back on the table.
She explained: "We need to make sure that Scotland is in its best position to make sure, that we can take advantage of the things that are important to Scotland in terms of the type of country we want to have, in terms of our economy, but also from a democracy point of view.
"It is really important that the people of Scotland have their choice bearing in mind it is 62% of people who voted to Remain.
"The choice has to lie not with politicians and the first minister - the choice really has to lie with the people of Scotland at that time - and at that time it is 18 months to two years time when we know the terms of the content of the Brexit deal is available."
Mr Tomkins acknowledged that the timing of a referendum was "really important".
He said the agreement made in 2014 for the first Scottish independence vote accepted the need for a timetable that suited both sides.
Mr Tomkins went on: "What happened last week could hardly be more different from that process of agreement we had in 2012 to 2014. Because what happened last week was the first minister of Scotland announcing some kind of unilateral demand that there had to be a second independence referendum.
"I think Theresa May as Prime Minister of the whole of the UK, including Scotland, is absolutely right to say now is not the time to ask this question again."
On the issue of Scotland's future Ms Hyslop said if the country was allowed to "drift" for the next two years it would definitely be out of the European Union.
Although he campaigned for the UK to retain its EU membership, Mr Tomkins said he now wanted the best Brexit deal for the whole of the UK.
In the Scottish Parliament earlier, First Minister Nicola Sturgeon insisted that Scotland's future should be decided by the people who live in the country rather than being "imposed upon us".
Scottish Conservative leader Ruth Davidson claimed voters were "sick to death of the SNP's games" over independence as the pro-UK opposition parties argued that there was no appetite for another referendum just two and a half years after the first one.
A second day of Holyrood debate on requesting a fresh referendum will take place on Wednesday with a vote of MSPs at 17:30.