Keir Starmer has promised to "reach out" to voters and earn their trust in the wake of Nicola Sturgeon's shock resignation.
The Labour leader said pro-independence supporters who had "lost faith" in the UK "have a point" and urged them to embrace his agenda to reform Westminster.
In a speech at the Scottish Labour conference in Edinburgh, Starmer started by giving a respectful nod to the outgoing First Minister, who quit last week.
"To lead Scotland for almost a decade is a political achievement that must be acknowledged," he said.
"And one thing we must always be clear about – wherever you stand on the constitutional question - we must respect those beliefs as a sincere desire to make the future better for Scotland.
“The First Minister was sincere about that and it shaped her service to this nation. And yes, it shaped her political success.”
He also admitted her success had been “grounded” in persuading former Labour voters to switch to the SNP:
“We’ve got to reach out to those people now.
“There will be people in your community looking again at the future of Scotland with fresh eyes. We have to meet their gaze with confidence.
“Show them - not just what the Tories and the SNP have done to this nation but the Scotland Labour can build a fairer, greener, more dynamic Scotland.
“We have to go out there and earn it.”
He added: “Prove - we understand the real concerns of the Scottish people. That we’ve listened to the reasons those voters lost faith in Labour and Britain and that we now offer the solutions that Scotland needs.”
He said of SNP voters who had “given up” on Labour and Britain:
“I know the people of Scotland want change and hope. Not a showy, grandiose hope - I don’t mean that.
“No, what I mean is the basic, ordinary hope, we used to take for granted. The sort of hope you can build your future around. That aspirations are made of."
He added: “Those Scots who lost faith in Britain. They have a point about Westminster. Britain has an economy that hoards potential and a politics which hoards powers. And these two problems feed off each other.”
However, despite a direct appeal to SNP voters, he again ruled out any coalition or pact with the Nationalists at Westminster:
“My message is the same: no deal under any circumstances.”
Although he acknowledged Sturgeon’s public service, he also attacked the record of her Government.
“Over fifteen years in power and what do they have to show for it? Honestly - it’s always somebody else’s fault and the reason is simple.
“They’re not truly invested in Scotland’s success. Anything Scotland achieves within the UK is met with gritted teeth. Seen as a roadblock to the one true goal. And so, they do nothing.
“It’s why standards in education are going backwards. Why the tragedy of Scottish drug deaths hasn’t been gripped.
“Why they haven’t just accepted Tory cuts to local services but piled on the misery. If it’s not about the constitution – they’re not interested.”
He also took aim at the Tory Government of Rishi Sunak, who he is trying to replace as Prime Minister.
“The pain they’ve inflicted to our economy and public finances. To our reputation around the world. To our NHS and public services. It’s immense.
“They’re not capable of the change Britain needs. And as for the cynicism of what they’ll do at the general election to try and claim political credit for the sacrifices working people are making now, it beggars belief.”
Scottish Tory MSP Craig Hoy said: “Keir Starmer is clearly desperate to win over SNP voters, which explains why he’s offering Nationalists more concessions on the constitution in the naïve hope this will satisfy them.
“Pro-UK voters are right to be alarmed by this, as they know Labour can’t be trusted to stand up to the SNP or for Scotland’s place in the UK.
“Labour are indistinguishable from the SNP on the big issues. They vote with the SNP at Holyrood most of the time, including when Anas Sarwar whipped his MSPs to vote for Nicola Sturgeon’s reckless gender reform legislation."
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