The SNP will continue to "frustrate what the government are doing as much as we possibly can", the party's Westminster leader has said.
Ian Blackford led a walk-out of his MPs during Prime Minister's Questions on Wednesday over the government's handling of the Brexit bill.
Opponents branded the move a "pre-prepared stunt" aimed only at furthering the cause of independence.
Mr Blackford said it was "not the end of the matter, it is the beginning".
The walk-out came after Speaker John Bercow expelled Mr Blackford from the chamber when the MP refused to sit down after asking for the Commons to sit in private.
SNP MPs were furious after amendments to the EU Withdrawal Bill affecting Scotland were passed after less than 20 minutes of debate the previous evening, with the only speech being from Cabinet Office minister David Lidington.
Mr Bercow has now granted the party an urgent debate on Brexit and devolution in the Commons, which will be held on Monday and last up to three hours.
Holyrood had previously refused to grant formal consent to the bill, with Labour, Green and Lib Dem MSPs uniting with the SNP to outvote the Conservatives.
The opposition centres on the bill "temporarily" constraining Holyrood's ability to use 24 powers that return from Brussels for up to seven years.
The UK government, which reached an agreement with the Welsh government over the issue, says this will ensure the same rules and regulations remain in place across the UK in areas such as agriculture and food labelling.
The remainder of the 153 returning powers will go straight to the Scottish Parliament, however.
Speaking in the Scottish Parliament, Nicola Sturgeon argued that this week's events had been "the most clear and powerful evidence so far that the Westminster system simply does not work for Scotland".
The first minister also repeated her claim that the Tories had "ripped up the convention that has underpinned devolution for nigh on 20 years" and predicted the party would pay a "heavy price".
The UK government has signalled that it wants to continue working with its opponents towards finding a resolution to the long-running row.
In a statement to MPs on Thursday afternoon, Scottish Secretary David Mundell said the powers at the centre of the row had been "handed to the European Union through our membership in 1972, long before devolution existed in Scotland".
They had therefore never been under the control of Holyrood, and it was wrong to argue that the powers had been "taken away" from the Scottish Parliament, he added.
Mr Mundell, who faced calls to resign from opposition parties, said the government would press on with its Brexit plans despite the lack of Holyrood consent, but insisted its aim was still for agreement to be reached between the two sides.
He added: "The Scottish government's position from the outset was that they would be content with nothing less than a veto. However, such an unreasonable position would fundamentally undermine the integrity of the UK internal market.
"We on this side of the house have compromised, we have made every effort to reach agreement. We have sought consent.
"Now, we are legislating in line with the Sewel Convention to ensure the whole of the United Kingdom leaves the EU with as much legal certainty as possible. That's what people and businesses in Scotland need."
The Sewel Convention states that the UK Parliament has the authority to legislate on any issue, whether devolved or not, but will "not normally" do so in devolved areas without the consent of the Scottish Parliament.
But Mr Mundell said: "I think anyone would accept the UK leaving the EU are not normal circumstances."
Speaking to the BBC's Good Morning Scotland programme earlier on Thursday, Mr Blackford said the SNP and Scottish government would mount a "very robust defence of our parliamentary democracy, our parliamentary sovereignty and the rights of the Scottish people".
He insisted Wednesday's walk-out, which was backed by Ms Sturgeon, "certainly hadn't been a stunt" and that the UK was now in the midst of a "constitutional crisis".
And he warned that a failure by the UK government to "think again" on the Brexit bill and its impact on the devolution settlement would see the SNP "take whatever action is necessary".
Mr Blackford added: "I will make sure that we can frustrate as much as we possibly can what the government are doing.
"We will remain civil, we will remain polite, we will remain courteous. But they need to understand that a line has now been crossed - the Conservatives are enacting legislation without the support of the Scottish Parliament.
"We are now in different territory."
Mr Blackford hinted that his party would next target the government's Trade Bill, which aims to ensure the UK can continue its existing trade policy as far as possible immediately after Brexit.
Scottish Labour MP Paul Sweeney also criticised Mr Mundell, asking: "If there is no agreement between the Scottish and UK governments, will he resign?"
Mr Sweeney also said it was clear that neither side had genuinely wanted to reach an agreement, and called for cross-party talks to resolve the dispute.
He added: "We have seen childish antics from the Tories when it comes to the programme motion, and we have seen childish antics from the SNP yesterday.
"The people of Scotland deserve better and they simply want this mess fixed by the politicians that they sent here to stand up for them before this shambles ends up in court."
Mr Mundell said his only regret was to see the "once proud" Scottish Labour Party move on to "nationalist territory" in backing the SNP over the consent row.