Following a meeting of opposition party chiefs, the SNP’s Westminster leader Ian Blackford said there was “a real focus from all of us that we must speak out against prorogation of parliament”.
A source close to the so-called 'Rebel Alliance' opposing a no-deal Brexit suggested MPs could refuse to leave the parliamentary estate, and the leaders of Labour and the Liberal Democrats in the House of Lords are reported to be boycotting the formal prorogation ceremony.
MPs are also set to vote a second time on whether to call a snap general election, with opposition parties set to reject Mr Johnson’s demand to go to the polls.
The Prime Minister's official spokesman said that while the Government would obey the law Mr Johnson would not be requesting another extension of the Article 50 EU withdrawal process.
"The Prime Minister is not going to seek an extension," the spokesman said.
"If MPs want to resolve this there is an easy way - vote for an election today and let the public decide."
Following the meeting of opposition leaders on Monday morning, Mr Blackford told reporters that the country was “in a constitutional crisis the likes of which we have never seen”.
“I think what’s striking is the language that has been used over the course of the weekend, and the clear indication that they are seeking ways to undermine the will of parliament and the rule of law,” Mr Blackford said.
“There are real questions that have to be answered by the two law officers… because of their responsibility to uphold the law.
“It is an absolute outrage that the government is sending a signal to the people of these islands that it’s perfectly acceptable to ignore the rule of law.
“The fact that a Prime Minister thinks its reasonable to behave in such a way is completely unacceptable.
“And it's in light of that that there is a real focus from all of us that we must speak out against prorogation of parliament.”
The SNP leader went on: “It’s really important that the people of the United Kingdom know the harsh reality, that this is not parliament against the people, it’s the Prime Minister shutting down the democratic institutions of the United Kingdom.
“There are real questions about the power of the executive, and the powers of a Prime Minister who at a whim, because he recognises he's in trouble, recognises he doesn't have support in parliament, chooses to shut Parliament down.
“This is as big a crisis as we could possibly imagine.”
And the SNP MP said opposition parties would look to collapse the government in mid-October, adding: “When we come back on 14 October, the first thing we’re going to face is a government coming forward with a Queen's Speech.
“There is not a cat in hell’s chance of the government getting that Queen’s Speech through. That in itself is going to trigger a general election… we’re absolutely desperate for a general election as soon as possible.”