First Minister Nicola Sturgeon has said she is "proud" of SNP MPS who staged a mass walkout of the House of Commons in a row over the EU Withdrawal Bill.
The row was prompted by a "lack of debate" on what Mr Blackford said was a "power grab" by the UK government.
The UK government accused the SNP of staging a political stunt just as they were about to be granted a debate.
The episode with Mr Blackford took place during the weekly Prime Minister's Questions session after he said it was a "democratic outrage" that MPs had not been given enough time for debate the Scottish government' concerns over the Brexit bill.
The long-running dispute centres on what happens to certain devolved powers when they return from Brussels, and has led to MSPs voting to withhold consent for the Brexit legislation..
Mr Blackford demanded the House sit in private, and was ordered out of the chamber by the Speaker when he refused to sit down. His fellow MPs then followed him out of the chamber.
The first minister and SNP leader Ms Sturgeon praised the MPs' actions, telling BBC Scotland: "The events in the Commons yesterday were a travesty of democracy.
"Stitch-up after stitch-up that were more about protecting the Tory party than protecting the interests of the country. Scotland was treated with utter contempt.
"The SNP MPs today made sure that issue was highlighted and they did it in the only way open to them.
"I'm very proud of Ian Blackford and the SNP MPs for making sure today that Scotland's voice was heard."
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Scottish Secretary David Mundell said the SNP was about to be granted a debate on the devolution aspects of the EU Withdrawal Bill, something which did not take place as a result of the walkout.
He added: "Disappointed, if not surprised, that if they really felt so strongly about it, they chose a stunt over holding the government to account."
The SNP later said it had attracted 1,000 new members in the immediate aftermath of the row.
Labour also accused the party of staging a walkout, rather then secure a debate on their grievances.
Shadow Scotland Secretary Lesley Laird said: ""Today's stunt by Ian Blackford and his colleagues simply emphasises further that they have one aim - to play political games rather than standing up for Scotland.
"They had a chance today to question the prime minister and secure a three-hour debate on devolution. Instead, they chose to flounce out of the House of Commons."
Ms Sturgeon said the SNP "did not make a habit of doing the kind of thing that was done today", but that Mr Blackford was "right to stand his ground".
'Convention ripped up'
She said: "If it was simply disrespect to SNP MPs, that would be one thing. But what we saw yesterday was deep disrespect for Scotland and it proved very powerfully that the Westminster system simply does not serve Scotland's interests."
The first minister said the relationship between the Scottish and UK governments over Brexit could no longer be "business as usual".
"The convention that has underpinned devolution for nigh on 20 years now has been ripped up by the UK government," she said.
"We will consider carefully ways in which we can continue to highlight the injustice that is being done to the Scottish Parliament and to Scotland...but always with Scotland's interests very much at heart.
"The real impact of what we have seen is that people across Scotland are under no illusion that the Westminster system, in which we were told Scotland was an equal and respected partner, simply doesn't work for Scotland.
"Our interests have been ignored, the voice and views of the Scottish Parliament have been completely cast aside, and I don't think it will be quickly or easily forgotten."
Mr Mundell, is expected make a Commons statement on Thursday on Brexit and devolution.
He will address MPs on the workings of the Sewel Convention, which recognises that Westminster will not normally legislate on devolved matters in Scotland, Wales and Northern Ireland without the consent of the Scottish Parliament, the Welsh Assembly or the Northern Ireland Assembly.