Ian Blackford told the BBC's Sunday Politics Scotland programme that they would not form a coalition with Jeremy Corbyn's party, but that they would be prepared to work with them on a "progressive basis".
The MP for Ross, Skye and Lochaber was asked if support for a minority government would depend on them being given a section 30 order - legislation which gives Holyrood the power to stage a referendum.
He replied that Mr Corbyn had to "respect democracy".
Mr Blackford added: "If the people in a Westminster election reinforce that by voting for the SNP, he has to respect that it should be the Scottish Parliament that determines when a referendum is called, not a government in Westminster.
"It is absolutely the case that everything that was seen going on at Westminster demonstrates that the people of Scotland have got to have the right to determine their own future - that means that we have to have that section 30 sitting in the hands of the Scottish Parliament."
Scottish Labour leader Richard Leonard said last month that the party would oppose a second referendum on independence in its next UK manifesto.
It came after Mr Corbyn said he would "decide at the time" whether to approve a section 30 order.
Shadow Chancellor John McDonnell has suggested a Labour government would not stand in the way of a referendum if there was support for one in the Scottish Parliament.