Ian Blackford said the crisis does not mean work on preparing for another vote has to halt.
It comes after Mr Blackford recently hinted at a possible delay to the indyref2 timetable.
Many do not believe there is any realistic prospect it will happen.
Appearing on BBC Scotland's Sunday Show, Mr Blackford was asked if anybody still believes there will be a referendum in 2023.
He said: "Let's remember, we fought an election last year, which the SNP won.
"We now have an agreement with the Greens. There's a majority for independence in the Scottish Parliament."
Pushed on the timing, he said: "Is anybody suggesting that Putin should determine the timeline for an independence referendum in Scotland?"
He added: "What I said is the focus of my attention today is making sure I do what I can to support those that need our protection from Ukraine.
"But that doesn't mean that the work in preparing for an independence referendum, to make sure that people in Scotland have got that choice - you know, one of the things I've talked about is about us wanting to welcome refugees, and the barriers that have been put there.
"I want to contrast the kind of outward-looking approach that an independent Scotland would have with the hostile environment that we continue to see.
"This week we will be debating a Bill in Westminster that is going to criminalise refugees. That's not a society I want to be in."
Mr Blackford was also asked about his position as leader of the SNP Westminster group, following reports he could be set to quit.
He said: "I've got a job to do and I've got the confidence of my colleagues."
Asked who is briefing against him, he said: "You might know better than me.
"I'm not aware of any MPs that are briefing against me."
At the Scottish Conservative conference in Aberdeen on Friday, Prime Minister Boris Johnson insisted it is "blindingly obvious" that now is not the time for a second independence referendum.