It comes after Mr Blackford walked out of the chamber on Monday before the speaker threw him out for refusing to withdraw his charge that the Prime Minister had lied and misled the house during Downing Street parties.
The SNP’s Westminster leader told ITV’s Good Morning Britain on Tuesday he took “no pleasure in having to leave the chamber” but he had “a duty to stand up on behalf of constituents”.
“It seems, I have to say, slightly perverse that I’m the one that is to be thrown out of the House of Commons on the basis of standing up and telling the truth,” he said.
“Now, if I had withdrawn what I’d said yesterday in the House of Commons I would have been guilty of doing what the Prime Minister has done, and that would have been lying to everybody watching.
“One of these days, the Prime Minister is going to have to accept that he has abused the trust that was put in him when he became Prime Minister. He should have gone by now.
“And this morning, my message to Tory MPs, they’re going to have to do the job because, quite simply, this man is not fit for purpose. He’s not fit to be Prime Minister.”
Mr Blackford also noted that a full publication of the Sue Gray report could be achieved ahead of the publication of Met police findings.
During an interview with BBC’s Good Morning Scotland, Mr Blackford said: "I have signalled that I will be putting down a motion and I will be asking other opposition parties to work with us and indeed other conservative MPs as well to make sure we get that.”
Questioned if he had any regrets about missing any of Monday’s debate, Mr Blackford said: “I regret that on the basis of being in parliament and doing my job – which is to call this Prime Minister out for his behaviour – that he came to the house of common on December 8 and said that no parties had taken place.
"He knew fine well that he had been to those parties.”
Mr Blackford denied that his walk out on Monday was a political stunt, adding: “What we are talking about is the truth and what we are talking about is a situation where there is no dubiety that this Prime Minister has misled parliament.
"We do not have to wait for the Sue Gray report. That is already there. He has already admitted he has been at these parties.
"There has to be dignity in public office
"I followed the previous Prime Minister Theresa May in the chamber yesterday and for all my criticisms of her or previous Prime Ministers, I certainly would never question her integrity, her decency, her moral code. That’s the difference with this Prime Minister.”