Ruth Davidson is appealing for Tory party members to put preserving the United Kingdom above their wishes on Brexit.
The Scottish Tory leader made the comments after a poll suggested a majority of Tory members would put Brexit ahead of preserving the union.
The YouGov survey of party members found that 63% would be prepared to see Brexit take place – even if it meant Scotland leaving the UK.
Davidson said Brexit should be delivered, “but not at the expense of breaking up the UK”.
She told BBC Scotland: “I think there are a number of people within the Conservative Party who need to take a long, hard look at themselves.
“Yes, I understand of course we have got to respect the referendum result, of course we’ve got to deliver Brexit, but not at the expense of breaking up the UK.
“I would remind people of their obligations within the party – yes, we’re a Conservative Party, but we’re also a Unionist party, and I’d remind them that our own union of nations is every bit as important as leaving someone else.”
The SNP said the poll findings were an “utter disaster” for the Scottish Conservative leader.
SNP depute leader Keith Brown said: “The Tory Party has clearly gone off the deep end – with their Brexit obsession pushing the party further towards the extremes.
“Tory members are so determined to deliver a damaging Brexit they are happy to watch our economy collapse and open the door of number 10 for Nigel Farage to take control of the UK.
“And far from prioritising the union, it’s clear Scotland means so little to the members of the Conservative and Unionist Party that two-thirds are happy for Scotland to become independent if it secures Brexit.
“With this poll suggesting that almost a quarter of Tory members in Scotland would prefer to deliver Brexit for their membership down south even if it means an end to the union, it’s becoming clearer that Ruth Davidson has little authority in her party in Scotland.”
Scottish Labour deputy leader Lesley Laird said: “The biggest threat to the union today is the Tory Party.
“Their members and their MPs would happily trade tearing our country apart in return for a chaotic no-deal Brexit.”
A spokesman for the Scottish Tories said: “Conservative members need to remember ours is a party of the whole UK.
“It’s in the name. If Scotland becomes independent, there is no UK.
“No matter how badly people want Brexit, no Conservative and Unionist member should be prepared to turn their back on the UK.”