Ruth Davidson expects all candidates for the UK party leadership to rule out a second referendum on independence.
It came as Nicola Sturgeon seized on the SNP's emphatic victory in the EU election in Scotland to warn that more Scots are being pushed towards backing independence.
The Scots Tory leader confirmed that she has had "multiple conversations" with candidates to replace Theresa May and has been seeking assurances about their plans to strengthen Scotland's place in the UK.
Asked if she would expect all candidates to rule out a section 30 order, transferring power to Holyrood to stage a second independence referendum, Ms Davidson said: "To be honest I would probably expect them to do that.
"We've yet to see the manifestos from any of them, so in terms of what they bring forward let me judge it when it comes.
"But I can't imagine there will be any of them that are running to grant it."
Mrs May announced her departure last week and a new leader is expected to be in place by the end of July.
The Scots Tory leader's endorsement will be viewed as vital for any potential candidates seeking to replace Mrs May, particularly as the party north of the border avoided the UK-wide collapse in the Euro elections and manged to retain its one MEP.
Ms Davidson added: "I have, and will continue to have, multiple conversations with multiple people who are considering or already declared to be running - some indecently early before the Prime Minister left, let me tell you.
"But those conversations will remain private because at a time like this you need to be able to have conversation s about where the party's head is and what people are looking for.
"I will, as will David Mundell, as will both elected MPs and MSPs be looking for assurances from all the candidates how they're gong to strengthen our United Kingdom, how they're going to advance and promote Scotland's interests both at home and abroad and crucially how they can bring out country back together.
"The real lesson from this European election UK-wide is how divided Britain still is."
The First Minister, speaking during an official visit to Dublin today, hailed the result as a "historic and spectacular victory" for the SNP.
She said: "The UK political system has failed - and it has failed Scotland utterly.
“Scotland said no to Brexit in 2016. This result makes clear, we meant it.
“The message from Scotland today is that we will not accept a Brexit process that silences our nation, that treats our parliament and government with contempt and that fails to represent the interests of people in Scotland.
“The SNP will continue working with other parties to stop Brexit and all the ensuing economic damage to Scotland.
“If all Westminster has to offer is more chaos and confusion – potentially under the Premiership of an extreme Tory Brexiteer – then more and more people will come to the conclusion that Scotland’s future is best served as an independent country.”