Theresa May will be warned her days as prime minister of the whole United Kingdom will be numbered if she fails to protect Scotland's place in Europe.
SNP MP Angus Robertson will insist Mrs May cannot "ignore the expressed will of the people of Scotland" as he launches his bid to be the party's depute leader.
Almost two-thirds (62%) of Scots who took part in last month's referendum on European Union (EU) membership voted to Remain.
Despite that, the UK as a whole voted in favour of Leave, with SNP leader and Scottish First Minister Nicola Sturgeon having warned the result makes another vote on Scottish independence "highly likely".
Mrs May has already indicated she is willing to listen to options that would allow Scotland to have a different relationship with the EU.
The Tory, who came to Scotland within days of becoming prime minister, said people there have ''had their vote'' on independence and this option should not be on the table
Mr Robertson has already claimed Scotland is "on the brink of independence" after announcing he wants to be Ms Sturgeon's second in command in the SNP.
Speaking ahead of his campaign launch in Edinburgh, the Moray MP said: "I am looking forward to setting out my case to be the next depute leader of the SNP.
"I believe that I am the best candidate to work with Nicola Sturgeon to deliver the collective goals of our party.
"It will be a chance for me to outline my priorities around leadership, grassroots and independence."
He added: "Last week I said that Scotland was on the brink of independence. Today, I'm going to deliver a message direct to our new Prime Minister, Theresa May.
"The Prime Minister can no longer continue to ignore the expressed will of the people of Scotland and I will tell members in Edinburgh today that if Theresa May refuses to even consider how we might protect Scotland's place in the EU, then she should be in no doubt that her days as Prime Minister of a United Kingdom are numbered."
Mr Robertson's most high-profile challenger for the depute leadership is Alyn Smith, the MEP who received a standing ovation in Brussels for his plea to EU members to respect Scotland's vote to remain.
Mr Smith has offered to be ''a freelance roving sherpa'' for Ms Sturgeon in Europe to get the best deal for Scotland. Other contenders are MP Tommy Sheppard and councillor Christopher McEleny.
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