Mike Russell stressed the need for UK ministers to seek a “very long extension” to the Brexit process.
As it stands, the UK is due to leave the EU on April 12, with no deal yet in place.
Prime Minister Theresa May is meeting Labour leader Jeremy Corbyn for a second round of talks in a bid to resolve the impasse which has resulted from the Commons’ repeated rejection of her Withdrawal Agreement.
But for progress to be achieved, Mr Russell said the PM would have to “move from the bunker” and accept some form of compromise.
Speaking on BBC Radio Scotland’s Good Morning Scotland programme on Thursday, Mr Russell said: “Jeremy Corbyn said last night he was surprised that the Prime Minister hadn’t given more, I’m not surprised. I think anybody with experience of the Prime Minister knows that she doesn’t give, she just sits there and takes.
“And I think that’s going to be the big issue, is she prepared to move from the bunker in which she has established herself over many months and move forward?
“There are no signs that she is, but equally those discussions will have to continue.
“She has kept the clock ticking in a very dangerous way. This is her responsibility.
“So there is a responsibility to try to find some way forward before the cliff-edge of a no-deal Brexit which is now essentially a week away.”
With the UK’s exit date - which has already been delayed from the original March 29 deadline - looming, Mr Russell revealed he had written to Mrs May’s defacto deputy, David Lidington, to argue the case for the UK taking part in May’s European Parliament elections.
He said: “Yesterday I wrote to David Lidington to say I thought those elections were now essential and have to be held.”
Mr Russell argued that “any solution” to the Brexit impasse had to have a People’s Vote “at the heart of it” - noting that politicians at Westminster had failed to resolve matters.
“The people have to be asked what they think,” he said.
But he stressed “you can’t rush a referenda”, insisting best practice would have to be followed for such a vote.
He said: “Clearly this is a matter of six to eight months, I would have thought, that also implies a very long delay and sensible people are arguing for that very long delay and for European elections.”
That could have knock-on implications for a possible second Scottish independence referendum - with First Minister Nicola Sturgeon set to make clear her thinking on this only when there is more clarity over Brexit.
Mr Russell accepted: “Quite clearly clarity on the Brexit process is required.”
But he also said: “Equally I have to say that I don’t think the people of Scotland should have to suffer the chaos and confusion and economic and other destruction that is taking place at the present moment.”