Ian Blackford said, however, that the number one priority of the Scottish Government right now is tackling the Covid-19 pandemic.
And he explained the “key” would be putting in place circumstances which would allow for an independence vote to be held.
Mr Blackford said: “I want to see that referendum happen as quickly as is practically possible, I think it’s in everybody’s interest that that is the case.
“But of course we’ve got to get the election out the way, we need to make sure that the SNP are elected back into government again, that we reinforce that mandate for a referendum.
“There’s a Bill that will be published over the coming weeks and that can be enacted once we’re on the other side of the election.
“Of course what I would say is that the first priority of the Government is dealing with the Covid crisis, it’s about keeping people safe, it’s about the acceleration that we’ve seen with the vaccine programme, it’s about taking off the measures of lockdown as and when we can.
“But we do that based on data, we do that based on evidence, we do that based on keeping people safe.
“When we’ve got to that position of safety, that would be the right time to have the referendum.”
He continued: “(Scottish Constitution Secretary Mike Russell) has talked about a six-month period once the legislation is triggered which could be in June, so it could be the case we could face a referendum as early as late 2021.
“But the key thing is that we put in place the circumstances that allow that to happen, whenever it happens, and that we have an inclusive debate with everybody in Scotland about the kind of country that they want to live in.
“And it is a choice of two futures. It’s the long-term damage of Brexit, it’s the impact of Tory austerity, or it’s about that economic recovery, that fairer Scotland, that greener Scotland that we want to see with Scotland being an independent country back into Europe.”
Mr Blackford also warned Prime Minister Boris Johnson that he “cannot stand in the face of democracy” in the event that the SNP wins a majority in the Scottish Parliament elections in May.
He said: “Democracy has got to prevail and there’s been a long-held, cherished position that in Scotland sovereignty rests with the people.
“There’s never been a situation in Scotland that sovereignty has rested with Westminster, has rested with Parliament, and you can go right back to the Declaration of Arbroath, the claim of right and everything that’s gone around that, that does demonstrate that in the end, it has to be about the will of the people, to be able to choose their own future.
“And I’d say to Boris Johnson or anybody else in the Tory party that they cannot stand in the face of democracy, they cannot stand in that will of the Scottish people to see their sovereignty enacted, to have that discussion, to have that debate and to make that determination as to whether or not we wish to be independent.
“And certainly that’s the case that if we win the election, and I’ll never take anything for granted, that we’d be making that case pretty robustly.
“We will support our colleagues in government in Edinburgh in making sure that we get what the Scottish people vote for.”
The SNP Westminster leader added: “I hope and believe that we can win a referendum and win it well, but I want to be able to bring Scotland together and there is a place for those that are on the other side to come on that journey with us and to contribute to Scotland’s story because it’s in all our interests to do that.”
Scottish Conservative leader Douglas Ross hit out at Mr Blackford, saying that pushing for another referendum as early as this year is “wholly irresponsible”.
He said: “The First Minister’s team claimed this week that it was irresponsible to try to remove her in the middle of a pandemic, despite all she’s done wrong.
“There is nothing more reckless and wholly irresponsible than pushing for another referendum as early as this year, when all our efforts should be on tackling Covid-19 and protecting jobs.
“We need to focus on the current crisis, not create a whole new one with another divisive referendum.
“The health crisis may soon be over thanks to the resounding success of Scotland and the UK’s vaccine scheme but the next great challenge, the economic crisis, is still to come.
“We need a Scottish Parliament 100% focused on dealing with that looming jobs and economic crisis. We must focus on rebuilding Scotland, not another divisive referendum.”
Responding to comments from Mr Blackford, Scottish Liberal Democrat leader Willie Rennie said: “Another independence referendum will do nothing for the hundreds of thousands of people whose operations have been cancelled, or the children whose education has been disrupted.
“This suggestion from Ian Blackford is not just divisive politicking at a time when the country should be coming together, it's a threat to divert resources away from the issues that really need it.
“Scottish Liberal Democrats will put recovery first with an election campaign based around health, education, jobs and tackling the climate emergency.”