The Tory peer Lord Forsyth has called for a structural rethink of the Scottish Conservatives after saying the party had become "marginal".
He said they needed a Scottish leader elected by grassroots members as well as better links with Tory MSPs.
Scotland Office minister David Mundell denied the Tories had become a marginal force, even through he is the party's sole Scottish MP.
But he said a wide-ranging debate over the future of the party was needed.
The aftermath of the UK election saw a Liberal Democrat MP, Danny Alexander, appointed as Scottish secretary.
A bit marginal
Speaking on BBC Scotland's Politics Show, Lord Forsyth said: "It's no good deciding, 'oh we'll have a great campaign for three weeks for a general election'.
"You've got to do this day-in-day-out and the Conservatives have got to be seen to be involved in the day-to-day issues in Scotland, and I'm sorry to say I think for a long time the Conservatives have been a bit marginal."
He went on: "There is no-one in charge, we need to have someone who is in charge of the Conservative party in Scotland. Preferably elected by the membership.
"The membership and the constituencies have been allowed to atrophy.
"The branches have disappeared, there's no real link between the voluntary side of the party and the MSPs and I think probably and I'm as guilty of that and everybody knows that I've been very sceptical about devolution.
"But I think probably we have to accept the reality of the Scottish Parliament and perhaps use that more effectively as a platform to put across our ideas."
Mr Mundell said demonstrating the Conservatives could govern well was a key issue for the party, which is led in Scotland by Annabel Goldie.
He added: "I think we need and welcome a debate about the structure of the party and a fundamental debate about how we approach politics in Scotland.
"I think we have to accept one in six people in Scotland did vote Conservative - yes we only got one in 59 MPs - but that doesn't make us a marginal force.
"In the Scottish Parliament we've been quite an effective force at influencing policy."
On Lord Forsyth's comments, Mr Mundell said: "One thing which I'm delighted to hear is that Michael Forsyth is now saying that we should embrace the Scottish Parliament.
"I hope that all strands of Conservative opinion in Scotland will now take heed of that and see that as a very important focus of taking the party's policy platform forward in Scotland."