His comments come as a new poll showed that two-thirds of Scots think that the Prime Minister should resign due to Partygate, alongside a boost for unionists with a 52/48 lead for No.
Mr Kerr was asked to explain why there was a different bar for the SNP/Green coalition in Holyrood versus the Liberal Democrat/Conservative coalition in Westminster in terms of having a democratic mandate.
He said: “There isn’t necessarily a different bar but it has to be realised that issues relating to the constitution are reserved and therefore it isn’t a straightforward matter.
"Our position remains that the SNP tested their manifesto commitment for a second independence referendum and they didn’t win a majority.
"All of the subsequent polling has shown, as highlighted by today’s poll in The Scotsman, that there is no appetite for this.
"It’s just not the will of the Scottish people.”
Asked if a majority in a future Holyrood election would be the point at which the Conservative party would agree there was a democratic mandate for indyref2, Mr Kerr said the “practical route” was a Section 30 order being approved by the UK Government.
When it was put to him that this was impossible due to the fact the SNP could never win a majority in Westminster, Mr Kerr added: “The SNP would need to get a majority in the Scottish Parliament as far as I am concerned.
"That would need to become the basis on which any future discussion we have, but I think Alister Jack has been quite clear in many respects about this issue as well.”
Mr Jack has previously said that 60 per cent of Scots would need to back a referendum in order for the UK Government to allow a referendum.
Mr Kerr also defended his party leader’s decision to withdraw his letter of no confidence in the Prime Minister and that he was given a “little prior warning” about the move.
However, he said the Scottish Conservative group, of which 27 of 31 MSPs backed Mr Ross in his calls for Mr Johnson to resign, was told “not as quickly as I would have liked them to be told”.
Asked whether he believed the Prime Minister was still fit for office, Mr Kerr refused to answer and said: "We’ll come back to all of that stuff, we’ve got to get through this global crisis.
"What this global crisis does is it gives us perspective.
"Right now what is important is that we unite...and that we support the Prime Minister and we support the government because actually the Prime Minister and the government have been doing all the right things.”
However, the SNP accused Mr Kerr of “shifting the goalposts”, labelling the comments worthy of a “democratic outrage”.
A spokesperson said: “In any other democracy - where the electoral system was designed expressly to prevent parliamentary majorities - this would be called out as a democratic outrage.
“But not in Scotland, Stephen Kerr and other leading Tories disrespect the all-party agreement in the 2014 Smith Commission with ridiculous shifting of the goalposts when they lose election after election, and then try to present it as a reasonable position.
“In May’s election the people of Scotland returned a majority of MSPs in favour of a referendum – greater than the one in 2011.
“If the Tories don’t like that, instead of undermining democracy, they should focus on how they can win an election in Scotland - something they’ve failed to do in Scotland for nearly 70 years."