Ian Blackford said Nationalist MPs would focus on scrutinising Brexit and opposing austerity, cooling SNP demands for a referendum by spring 2019.
But Mr Blackford insisted the party was not giving up on the ultimate goal, despite losing 21 seats at the general election, saying the SNP remained “the party of independence”.
The First Minister is expected to give an update on the Scottish Government’s call for a second vote on Scotland’s future this week after spending time “reflecting” on the general election result.
A spokesman dismissed reports that she will put another referendum on the back burner as “entirely speculative”. However, senior party figures were quoted yesterday suggesting that independence would now be presented as “a choice we can exercise in future” and an “insurance policy” in the event of a harsh Brexit settlement.
And another source told Scotland on Sunday that if the UK’s Brexit deal “includes formal membership or de facto membership of the single market, and such a compromise was reached, there would be no basis to have another independence referendum at this stage”.
The Scottish Government has already made a formal demand for the powers to hold a second independence referendum, ruled out by Prime Minister Theresa May.
Speaking on the BBC’s Sunday Politics Scotland, Mr Blackford said: “One of the things I think is important is if we’re going into the Brexit negotiations we need to wait and see what the outcome of that is. What we have continually said is that the people of Scotland, just like the members of any other European nation … should be able to have their say on the final outcome of Brexit.”
He added: “What I’m doing is concentrating on the job I have, along with my colleagues at Westminster, which is standing up for Scotland. It’s making sure we get the best deal for Scotland out of Brexit, challenging the Tories on austerity and, of course, the SNP is the party of independence.”
The First Minister set out her timetable for a second referendum in March, saying a vote should be held between autumn 2018 and spring 2019. But she has been “reflecting” on plans to hold another independence vote after the snap general election saw her party’s share of the vote fall from 50 per cent to 37 per cent.
The issue was discussed at the Scottish Government Cabinet meeting last week, with Ms Sturgeon “likely” to set out her position before the Holyrood recess at the end of June.
A spokesman for Ms Sturgeon said: “Reports in today’s newspapers are entirely speculative. We have always made clear our view that the people of Scotland should have a choice at the end of the Brexit process and the First Minister will set out her views on the way forward in the coming days.”
Opposition politicians at Holyrood insisted the SNP should drop plans for a second referendum “once and for all”.
Scottish Conservative deputy leader Jackson Carlaw said: “Rather than kicking Indyref2 into the long grass, Nicola Sturgeon needs to take the threat of a second independence referendum off the table altogether. The threat of an unwanted second referendum would only provide more uncertainty and risk.
“If Nicola Sturgeon wants to show that she really is listening to Scots then she needs to ditch these plans once and for all and get back to the day job.”
James Kelly, Scottish Labour’s election campaign manager, said Nationalists had not yet “cleared up confusion over the future of another independence referendum”.
He said: “Just hours after reports that Nicola Sturgeon is willing to put a second referendum on hold, her Westminster leader refused to say anything about a referendum on TV.
“All this confusion and distraction is eating up the energy of a government with a failing record.
“This confusion and dithering needs to stop. Nicola Sturgeon needs to rule a referendum out this week, and pledge to get back to the day job.”
Scottish Liberal Democrat leader Willie Rennie said: Nationalists were “keeping the referendum on the table because for the SNP will always be independence first and foremost”.
He said: “If the First Minister wants to respect the message she was sent on 8 June then she must cancel her plans for another divisive independence until at least the end of this parliamentary term.”