Ruth Davidson has urged party colleagues to back the Prime Minister following the resignations of Boris Johnson and David Davis.
The Scottish Conservative leader said Tory MPs should put their “shoulders to the wheel” in support of Theresa May and the “sensible” Brexit plan agreed by senior ministers at Chequers last week.
Ms Davidson said it was right for the Foreign Secretary and Brexit Secretary to go if they could not observe collective cabinet responsibility over the plan.
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First Minister and SNP leader Nicola Sturgeon has described the Brexit turmoil engulfing the UK Government as a “shambles” while the party’s Westminster leader Ian Blackford MP said it had become a “chaotic circus”.
In a statement released after Mrs May delivered her own statement to the House of Commons, Ms Davidson said: “At this vital time for our country’s future, people across Britain want - above all - a UK Government negotiating with one voice on the Brexit deal it seeks to achieve.
“I support Theresa May in leading such efforts in the days ahead.
“The Prime Minister made clear this weekend that collective cabinet responsibility must be observed on Brexit.
“If individual ministers can’t sign up to that, then it is only right they are no longer part of the government.”
Ms Davidson described the Chequers plan as “a sensible compromise approach, which both respects the referendum result to leave the EU while offering pragmatism on trade, skills and regulation.”
She added: “For Scotland, those proposals will provide business with frictionless access to the EU, ensure we leave the Common Fisheries Policy and make clear there will not be a border in the Irish Sea.
“This all helps to bolster Scotland’s biggest and most important market, the UK internal market.
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“I believe therefore that the Prime Minister deserves our support as she prepares for the upcoming tough negotiations with the European Union.
“I would urge colleagues to put their shoulders to the wheel in supporting the Prime Minister in that job.”
Scottish Secretary David Mundell said: “The Prime Minister has set out the Cabinet’s agreed UK position as we go into our negotiations with the EU.
“These are proposals which will bring significant benefits to Scotland and the whole of the UK, and I urge everyone to get behind them.”
However, Scottish Conservative MP for Aberdeen South Ross Thomson, who campaigned for a Leave vote, said he was concerned about the plan and said he was “proud”of Mr Davis and Mr Johnson for “standing by their principles”.
Writing on Twitter, he said: “The Brexit plan opening offer appears so diluted that we would be a vassal state.
“The decisions we take now will shape Britain’s relationship with the EU and the rest of the world for a generation. It’s imperative we do Brexit right no half measures!”
Mr Blackford said Mr Johnson should have been sacked earlier for being “a national embarrassment”.
He said: “His resignation shows the absolutely chaotic circus this government has become and shows a Prime Minister with no authority.
‘’At this absolutely crucial moment the Tories should be focused on the Brexit negotiations, but yet again they are all putting their own selfish political interest ahead of the interests of the country.”