The MP for Ross, Skye and Lochaber warned his party would only succeed if “united”, with the declaration coming after he was replaced by Stephen Flynn this week in what some MPs consider a coup.
The change in leadership prompted senior MPs Pete Wishart and Stewart McDonald to quit the front bench. Mr Flynn won in a secret ballot of SNP MPs on Tuesday, seeing off a challenge from Alison Thewliss.
Speaking exclusively to The Scotsman, Mr Blackford said he had a “range of emotions” over his exit, but insisted his focus would not waiver from delivering independence.
He said: “From my point of view, it is a party that is united. Parties that are not united won’t appeal to the popular support we need.
“We were elected to get Scotland out of the Union. I will focus on that and support those who have succeeded me.
"People across the Commons, both Labour and on the Tory side, have been very gracious. Both [Sir Keir] Starmer and Rishi [Sunak] have been in touch, which was very gracious.
“I’ve moved on. I've got my role as the First Minister’s business ambassador, it’s important that Westminster is able to move forward. I will work with everyone in that leadership team to make sure that happens.
“I felt that if I put myself in front of the members I could have won that [leadership election]. It’s a situation where I've got a lot of people who were very loyal to me and supportive and, of course, when something like this happens, [there’s] going to be a bit of difficulty. When any new leader comes in, they’re going to want to make decisions on their own team.
“There is a degree of anxiety, but people will be put in their new positions and move on.”
Asked if there was a moment that made him decide to stand down, Mr Blackford said it came after a conversation with First Minister Nicola Sturgeon where she agreed to give him a new role leading on business engagement for the SNP’s independence campaign.
He said: “What happened last week, having conversations with the First Minister, we’ve talked a lot over the years. I get frustrated by the ongoing arguments about the process and desperately want to get into a debate about what type of country we can be.
“I said to her ‘will you give me this job, focusing on this side?’ And I didn’t have to finish the sentence, she just said ‘yes’. That’s why I made the decision.”
Despite stepping back from the SNP front bench, Mr Blackford insisted he would stand again at the next general election.
He said: “I’m not in the first flush of youth. I’d like to think I've got some key strengths that can help the party and help the movement.
“I’m not going away, I'm just going to be in a different role, and I’m still intending to stand in the next general election."
The former SNP Westminster leader had relinquished his role amid reported frustrations within the party around a range of issues. These are understood to have included the handling of the sexual harassment allegations made against Patrick Grady, the former SNP chief whip, alongside feelings of detachment from the SNP’s centre of power in Holyrood.
Mr Blackford claimed he now had more time to focus on aspects of the independence debate.
He said: “I enjoyed doing it [the Westminster role]. I’ll always be grateful for the opportunity to represent constituents, represent the party, to use that voice that you have in that chamber to talk to people, not just people on same side as you.
“But this is a convenient jumping off point, and the things I am passionate about are getting to the heart of how we can change Scotland.
“I am angered by the outcomes for people’s lives in Scotland, people trapped in poverty. Life opportunities are limited and I’ve realised this change is releasing myself so that I can engage more meaningfully in that debate.
“If I’m right about where that potential lies, about how you create the wealth to drive up living standards and deal with ingrained social problems that we’ve suffered from, if stepping down gives me time to do that, then maybe some good comes from it.”
The 61-year-old, described by colleagues as a “workaholic” they had to prise out of his chair, said no longer being leader meant he was looking forward to more time with his family.
He said: “I’ve got to reflect on the fact I won’t be standing up and holding the Government to account in the same way, and I have mixed feelings about that. But, and I’ve never made a thing about this, given I live where I live, in the Highlands, it’s a nine-hour journey back and forward.
“Given I had to be down in Westminster an awful lot of the time, that’s meant my home life had to be sacrificed to a certain extent. The fact I’m going to be able to spend a bit more time with my wife is something I’m really looking forward to – to an extent getting my life back.”
Mr Blackford also heaped praise on the new SNP deputy leader Mhairi Black, who he was elected alongside in 2015, calling her a “fantastic campaigner”.
She replaced Kirsten Oswald, who stood down after two years in the role, having herself replaced Kirsty Blackman.
Mr Blackford said: “We came into Parliament in 2015 together and were a team. I was pensions spokesman and she was my deputy.
"As the youngest MP, I wanted to make sure she was supported and, to an extent mentored her. She’s someone I’ve got great affection for.
"She knows she personally has my support and can come talk to me anytime.”