Michael McMahon, who has been in Holyrood for 15 years, said his party must “not shirk for discussing a more far-reaching approach to devolution”.
He spoke out ahead of the first meeting of a new group of Labour activists, who want the party to consider changing its name in Scotland to the Independent Labour Party.
The Labour for Scotland group backs Holyrood being given full control over income tax, as well as complete responsibility for welfare - a position which goes further than Labour’s existing plans for further devolution.
It also states the party should pledge not to work with the Conservatives in any future Scottish independence referendums or “any other party whose policies are fundamentally at odds with the views of people in Scotland”.
Scottish Labour must be “fully autonomous from its London leadership”, it argues, suggesting the party north of the border should have the right to appoint its own full-time officials and write its own constitution.
Former MSP Pauline McNeill, Unison’s Scottish organiser Dave Watson and Scottish Trades Union Congress deputy general secretary Dave Moxham are all due to speak at the group’s meeting in Glasgow tomorrow afternoon.
It comes after large numbers of people in traditional Labour heartlands, such as Glasgow and North Lanarkshire, voted Yes in the referendum.
Mr McMahon, the MSP for Uddingston and Bellshill, said: “I sense a real desire in the Scottish Labour Party that, having fought successfully to maintain our place within the wider British Labour movement, for us to rediscover our core purpose and convince our fellow Scots that Labour remains the best route to delivering social justice for Scotland.
“We should not shirk from discussing a more far-reaching approach to devolution, not just to Holyrood, but also to local government, and we must explain how we will use any new powers to deliver a more extensive agenda on social justice.
“We should, therefore, welcome discussion forums that widen our opportunity to debate how to do this”.
Helen Williams, the secretary of the Clydebank and Milngavie constituency branch of the Labour Party said: “The referendum campaign showed us that people want to see a change in the way we do politics in Scotland.
“We need a debate among members from the bottom-up to make sure that we rise to the challenge and set out an ambitious 21st century vision of home rule that gives people much greater power over their own lives.”