The Nationalist leader at Westminster said his party would “welcome” another election if the Prime Minister’s proposals for exiting the EU failed to protect Scotland’s interests.
Mrs May is due to publish a Government white paper on her Brexit plans next week, despite the turmoil caused by the resignations of David Davis and Boris Johnson.
The agreement reached at Chequers last Friday includes plans for a free trade area for industrial and agricultural goods, based on a “common rule book” and a “combined customs territory”.
However, there will be different arrangements for trade in services including financial products, with the UK recognising neither side will enjoy “current levels of access” to each other’s markets.
Mr Blackford said if Mrs May did not alter her plans to bring them closer to this position, the SNP would “relish” the chance to fight another election.
“If we’re talking about a situation where the Scottish economy is going to be threatened and if there’s an opportunity for us to have a debate with the people of Scotland, then of course I would welcome that,” he told the broadcaster.
“My focus in the short term, my party’s focus…is about protecting the interests of the Scottish people. That’s about making sure that we stay in the single market and the customs union.
“If we faced an election as we go through that process then so be it, it’s something I would relish and something I would look forward to. I believe the SNP would come out of that in a strengthened position.”
Challenged over the result of last year’s snap general election, which saw the SNP lose 21 seats in Scotland including those of Alex Salmond and Angus Robertson, Mr Blackford was defiant.
“The SNP are still the dominant voice, the dominant party in Scotland. We’ve been the government party in Scotland for the last 11 years,” he said.
“I would firmly believe that if we had to put ourselves in front of the electorate again, we’d get the overwhelming backing of the people of Scotland.”