Scottish Secretary David Mundell and Jackson Carlaw, the Scottish Conservative party’s interim leader, described the deal to leave the EU as “the right plan for Britain and Europe”.
The SNP described the pair’s support for the deal as “sickening”, saying every Brexit outcome will see Scotland worse off.
The Conservative politicians spoke out just days after Prime Minister Theresa May accepted that the UK may not leave the EU on March 29, offering MPs a chance to vote to delay Brexit if her deal is rejected again later this month.
Mr Mundell and Mr Carlaw said: “The time for debating and negotiating is nearly over. The time to decide is here. Our clear position is that, over the coming days, MPs should decide to back the Prime Minister’s Brexit deal.
“It delivers on the decision the country made. It hands back control of our money, laws and borders.
“It gives us control over our waters, offering us the chance to revitalise our fishing sector. And, while we will be able to strike new trade deals around the world, the deal will also set the basis for a strong and abiding new friendship with our allies across the continent.
“It’s the right plan for Britain and Europe. Supporting it will mean we can all move on to meet the pressing and urgent challenges we all face.”
Meanwhile, at Holyrood, a Scottish Government debate on the EU withdrawal negotiations is scheduled to take place on Tuesday.
The senior Conservatives claimed First Minister Nicola Sturgeon will be making “one last attempt to wring yet more grievance out of Brexit” and boost support for Scottish independence.
Mr Mundell and Mr Carlaw added: “The best way now to stop the SNP’s separatist games is to back the deal, leave the EU in a smooth and orderly fashion, so we can all get back to the real task of creating a fairer, more prosperous United Kingdom.”
The SNP’s Europe spokesman Stephen Gethins responded: “The Prime Minister’s deal is bad for Scotland and the support from the Scottish Tories is sickening - they are clearly rattled and saying anything to try and deflect from their shambolic handling of Brexit.
“They have no higher ambition for Scotland than meekly accepting whatever Brexit disaster awaits the UK. Or as one of Mr Mundell’s own Cabinet colleagues put it - ‘Once you’ve hit the iceberg, you’re all on it together.’
“Every single Brexit outcome will see Scotland worse off - our nation overwhelmingly rejected Brexit at the ballot box and it beggars belief that Tory MPs and MSPs could advocate backing a botched deal that would see jobs, living standards and household incomes slashed and threatens the growth of our economy.
“There is a better future for Scotland, as an independent nation, and the fiasco of Brexit only serves to show how Scotland’s interests are ignored by Westminster.”