Ian Blackford said he was “gratified” that the focus was no longer on the timetable of such a vote.
Following the general election, First Minister Nicola Sturgeon announced plans for a second referendum were being put on hold.
She said it is still “likely” there could be another ballot before 2021, but told the Scottish Parliament she was going to “reset” the timetable which could have seen a referendum take place between autumn next year and spring 2019.
SNP Westminster leader Mr Blackford said rebuilding the case for independence needs to “promote fairness and equity” while pointing out “harmful” Conservative Government policies.
He told the Sunday Herald newspaper: “I think that what has happened as a consequence of Nicola’s statement is that we’ve taken away the focus from the timetable now and I’m gratified that gives us the opportunity to actually talk about the fundamentals and to talk about what an independent Scotland would look like. And I welcome that over the coming years.
“I joined this party because I believe in independence and it’s up to us to win the trust of people in Scotland and we’ve clearly got a manifesto commitment from the 2016 election that says if there is a change in circumstances, there’s the question of a second referendum.
“I think it’s a key task for all of us to compare and contrast the powers that we have and also demonstrate how we could do so much more [with independence] to promote fairness and equity.
“One of the things is to demonstrate how this Conservative government is pursuing policies that are harmful to Scotland.”
The Scottish Tories said the SNP have not listened to voters.
Shadow finance secretary Murdo Fraser said: “These latest comments from the SNP prove once and for all that they will always put independence first.
“Despite voters sending them a clear message this year that they are fed up with them obsessing over independence, the SNP just aren’t listening.
“It destroys claims from Nicola Sturgeon that her priority is anything but separation, or that she would be getting back to the day job.
“People are crying out for the Scottish Government to start concentrating on improving our hospitals, schools and the economy.
“But instead, we have a narrow-minded administration that will stop at nothing until they have torn Scotland out of the UK.”
Scottish Labour’s economy spokeswoman Jackie Baillie said: “It appears Ian Blackford didn’t get Nicola Sturgeon’s memo that indyref2 is on hold, and he certainly didn’t get the message from voters that Scotland is firmly opposed to a divisive second independence referendum.
“It just proves that the SNP is willing to continue neglecting our struggling health service, schools and economy. Scotland deserves better than this failing Government.
“There is nothing left-wing about the case for independence. It would cause £15 billion of cuts from day one, leading to turbo-charged austerity and punishing working families.
“The true left-wing alternative to the Tories is a Labour government that will work for the many, not the few, across the entire United Kingdom.”