Des Browne, the Scottish Secretary, was yesterday drawn into cross-party talks about changes to Scottish home rule.

Labour, LibDem and Conservative leaders at Holyrood met for the first time yesterday, and agreed the next stage will be to draw in their Scottish leaders at Westminster.

The inclusion of Mr Browne, who has previously expressed strong resistance to opening up the Scotland Act to further reform, is significant as a rare sign that the UK Government has shown any willingness to think again about current arrangements.

LibDem leader Nicol Stephen is eager to set up a new grouping that would consider further devolution, with suggestions of taxation powers going as far as a Scottish share of North Sea oil revenue.

He angered other parties ahead of yesterday's talks by seeking to push their agreement to talk further than they had agreed. There is opposition to a LibDem plan to set up a Scottish Parliament Committee, with a stress from other parties that progress has to be made by working with Westminster and the public more widely.

Sources close to Mr Browne lowered any expectation of a new constitutional convention or commission, saying discussions are at a very early stage and there should be no expectation they will move fast or reach any agreement. "If they can work together to frustrate the SNP in stampeding people towards independence, that's all to the good," said a Labour source at Westminster.

While LibDems at their Brighton conference yesterday reaffirmed their support for more powers to be devolved to Holyrood, Scottish Tory leader Annabel Goldie has recently discussed the way ahead with Shadow Chancellor George Osborne and with Shadow Scottish Secretary David Mundell. Tories shifted two years ago to agree there should be a review of devolved powers, while Labour has been most resistant to changing the settlement it introduced in legislation nine years ago.

In a brief statement after Ms Alexander, Miss Goldie and Mr Stephen met yesterday, they said they had held a constructive meeting, and that they are "committed to a strong Scotland within a strong United Kingdom".

It added: "The character of the meeting was exploratory about taking forward a mature and reflective discussion on strengthening devolution. There is complete agreement about this discussion progressing within the framework of the United Kingdom. The next step is engaging with our UK colleagues at Westminster and to that end we propose to meet jointly with Des Browne, David Mundell and (LibDem Orkney & Shetland MP) Alistair Carmichael."

The joint talks have been welcomed by the Scottish National Party, as a sign that its rivals have "signed up" to the argument that parliament needs more powers to be more effective.

First Minister Alex Salmond said: "There's clearly a dynamic at work there. We see that dynamic being very much in the context of the national conversation and look forward to it moving forward."