The YouGov survey for The Times Scotland found the Scottish Conservatives have retaken second place on 27 per cent - up 4 per cent from the last poll - while Labour have dropped 5 per cent to 23 per cent in Westminster voting intentions.
Despite the SNP and Tories both growing in support by 4 per cent since January, a seat projection from the poll gave the SNP 43 MPs - up from the current 35 - but saw the Tories drop two seats to 11.
Labour would lose six seats and be left with just one MP, according to the poll of more than 1,000 Scots carried out at the start of June.
However, a similar seat projection on the proportional system Scottish Parliament would see the SNP lose nine seats despite an increase in voting intentions for the party.
The projection would see the Greens pick up three seats and Labour, Lib Dems and Tories pick up two each.
Deputy First Minister John Swinney said: “This is an extraordinary endorsement of our record in government, with people continuing to put their trust in the SNP to deliver for Scotland.
“But it also shows that we’re winning the argument over Scotland’s future - how best we keep driving our country forward, delivering the best public services anywhere in the UK and building a fairer country.
“Our vision to create a successful economy and flourishing, inclusive society could not be further at odds with despair and chaos of Brexit from the Tories.
“But these figures will make dismal reading for Labour. They’ve got no credibility on the serious issues we face as a country, Richard Leonard is a struggling leader and that’s why they’re plummeting in the polls.”
The poll found Mr Leonard’s approval rating was -20 while UK party leader Jeremy Corbyn has an overall -30 rating among Scottish voters surveyed.
Ruth Davidson was the only senior politician with a postive rating at 11. Theresa May scored lowest at -44 with Nicola Sturgeon on -2.
The poll recorded no change in support for independence from the 45 per cent in the 2014 referendum.
Support for a referendum in the next five years stood at 40 per cent, with 52 per cent against and 8 per cent unsure.