Stephen Flynn is urging opposition supporters to lend their support to the SNP at the next general election, which will be held before 2025, to avoid "wasted" votes.
Scottish Labour deputy leader Jackie Baillie has called the plea a "desperate ploy" amid a turbulent few weeks for the SNP following a police probe into its finances and a search for auditors.
Mr Ross won the Moray seat in 2019 with a reduced majority over the SNP, with 22,112 votes, a decline in the vote share of 2.2%.
Meanwhile, Scottish Secretary Alister Jack beat the SNP by 1,805 votes in Dumfries and Galloway, while West Aberdeenshire and Kincardine MP Andrew Bowie, who is also under secretary of state for exports, was re-elected in 2019 with a reduced majority of 843.
"The SNP is the main competitor in every Tory-held seat, and the incumbent in every target seat - so a vote for the Labour Party or the Liberal Democrats is a wasted vote that risks letting the Tories in the back door, just like it did last time.
Ms Baillie, however, said: "As they watch their own vote share collapse, it is no surprise that the SNP has turned to such a desperate ploy.
"This is a move from a party that is mired in scandal, out of touch with Scotland and scared for the next general election.
Scottish Liberal Democrat MP Christine Jardine also said the comment "smacks of desperation".
She added: "A vote for the Liberal Democrats means getting politicians who put the issues that matter front and centre of the agenda, from battling the crisis in our NHS to cleaning up the sewage in our rivers and getting islanders the ferries that have never arrived."
Craig Hoy, Scottish Tory chairman, said: "The SNP have cottoned on to what Scotland's voters already know - that the Scottish Conservatives are the only credible threat to the nationalists in a large number of seats up and down Scotland.
"Only we can keep them out in numerous Westminster constituencies - not Labour or the Lib Dems.
"The SNP recognise that fact and are fearful of it. That's why they've made this desperate plea to pro-Union voters.
"But it won't work because those voters are sick and tired of the SNP ignoring the public's real priorities - like the cost-of-living crisis and unacceptable NHS waiting times - to relentlessly push their independence obsession."
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