Tory leader Ruth Davidson wants to use the party's success in today's council elections as a platform to mount a "fightback against the SNP" in next month's general election.
The Tories have gained more than 100 seats across the country with about two-thirds of the councils having declared, while the SNP has lost more than a dozen.
It consolidates the Tory comeback north of the border after last year's Holyrood election saw the party more than double its tally of MSPs to become the second party in Scotland.
Ms Davidson said the key indicator for next month's general election was how the "first preference" votes fell in today's council ballots.
The Tory leader said: "If you look right across the Borders, at Dumfries and Galloway, East Renfrewshire, in places like Perthshire, Aberdeenshire and in Moray - that's Angus Robertson's seat the SNP group leader...at Westminster, you see it's the Scottish Conservatives who have topped that poll.
"So we need to use this as a platform to take this fight to the SNP and lead Scotland's fightback against the SNP."
Ms Davidson added: "We've got to continue to work hard and we take nothing for granted and it's very different elections north and south of the border."
The Tory leader rejected criticism that her campaign for the local election was built on opposition to a second referendum and said the "simple way" to avoid this would be for the SNP to drop demands for a second referendum on independence.
"People right across Scotland who are looking for this Scottish fightback against the SNP, when they try to create a sense of momentum and hegemony, know that right wherever you are from the Borders to the Highlands, the only party strong enough to lead that fightback against the SNP is the Scottish Conservatives."