Speaking on BBC Scotland's Sunday Show, energy minister Greg Hands said he has a "very, very good relationship" with leader Douglas Ross and rejected suggestions that Mr Ross - who has called for Boris Johnson to resign over the Partygate scandal - should "wind his neck in".
However, Mr Hands also insisted that Prime Minister Boris Johnson has done some "great things” in his leadership, despite a growing lack of support for his continued leadership.
It is expected that Mr Johnson could face a no confidence vote from MPs as early as this week.
Mr Hands’ comments came as former Tory leader Sir Iain Duncan Smith defended Mr Johnson as the right person to lead the Tory Party into another general election and urged him to "sort this whole crisis out".
Mr Hands said he believes that the Scottish Conservatives will perform well in this year’s local elections in May, citing an "anti-Scotland" energy policy by the SNP government.
He said: "I talk all the time with Douglas Ross and other Scottish Conservatives. We have a really good relationship in terms of energy, which is my brief.”
When asked if Mr Ross should "wind his neck in” about whether Mr Johnson should stand down, Mr Hands said: "It is perfectly fine for Scottish Conservatives to have a different view on certain things".
He added: "I think the Scottish Conservatives will do very well in May this year. The SNP Scottish Government has been failing in areas not least like energy, their opposition to nuclear, their failure to support oil and gas .They are pursuing a very anti-Scotland policy when it comes to energy. So I think our chances as good.”
However, he dodged questions on whether Mr Johnson should campaign in Scotland.
He said: "I think we’ve plenty of campaigning forces on the ground. We've a fantastic campaigning arm in Scotland and I have every confidence in their ability to deliver a good result in May."
Speaking to BBC's Sunday Morning programme, Sir Iain opposed the prospect of a leadership election and said the partygate saga and its fallout were distracting from issues like the cost of living crisis.
He warned that "internecine warfare" culminating in a vote of no confidence should not be the priority while the cost-of-living crisis escalates.
"My sense right now is that if we go and plunge ourselves into a leadership election, vote of confidence - which in the end always damages leaders even if they win it - and then maybe a leadership election, internecine warfare, in the midst of which we're facing a big cost of living crisis...(getting that) sorted, that is our number one priority," he said.
He said other political players who may be vying for a leadership bid should "temper their ambition".
Asked whether Mr Johnson was the "right person to lead the Conservative Party" into the next election, Sir Iain added: "Well I do at the moment, that's why I said that as far as I'm concerned the Prime Minister is the one that has to sort this out.”