Tim Farron has urged SNP supporters seeing their vote being used to “chase a second referendum” to join his party.
The Liberal Democrat leader called on the “thousands of liberals in other parties” to defect in his first conference speech at the helm.
He also paid tribute to the late Charles Kennedy, before unleashing an impassioned attack on David Cameron’s “pitiful and embarrassing” response to the migrant crisis.
Mr Farron told activists in Bournemouth: “From the mouths of too many politicians come words of division, separation, spite and displacement.
“If you think that is wrong, if you reject the politics of blame and separation, if you say Britain is best when Britain is together … guess what?
“You are a liberal. Embrace that diagnosis. It is an entirely decent and utterly British condition.
“Maybe you are currently in the SNP and you see your vote being used to chase a second referendum, while devolved services like the NHS are creaking at the seams.
“If you are a liberal-minded person in another party which is not what you would want it to be, join us.”
Remembering the former Ross, Skye and Lochaber MP Mr Kennedy, he added: “Charles’s death has robbed us of the sharpest mind, the wittiest tongue and the nicest bloke.
“Charles, who led us to our largest number of MPs in living memory; Charles, who took on every corner of the establishment and led the campaign against the illegal Iraq War.
“Charles, we are so proud of you, and we will rebuild and we will fight back and we will do it in your honour.”
His remarks came hours after activists paid their own tribute to Mr Kennedy at the party’s infamous Glee Club.
Controversial songs referring to Mr Kennedy’s drinking were not sung by members, despite being published in the annual Liberator lyrics book.
At the general election, the Lib Dems were reduced to a rump of just eight MPs as voters turned their back on the Conservatives’ coalition partners.
But Mr Farron told activists they should be prepared to return to power in 2020 – even if that meant another alliance with the Tories.
He said his party should be “serious about power” and claimed the election of Jeremy Corbyn as Labour leader had left the Lib Dems as the only credible opposition.
“Against all the odds, we have just been given the chance to take centre stage,” he concluded. “We will take that role.”
Looking ahead to elections in Scotland, Wales, local councils and London next year, he said the mission was to put Lib Dems back in power at every level throughout Britain.