Critics say the plan would undermine universal mail delivery and risk jobs
The Scottish Labour Party chairman has opposed any form of privatisation for Royal Mail.
Dave Watson told Labour's annual conference the proposed 30% sell-off failed to keep a manifesto commitment to a publicly-owned Royal Mail.
UK Business Secretary Lord Mandelson said the plans were needed to ensure the post continued to be delivered.
Scottish Labour's leader said he backed the plan if it made Royal Mail more efficient and secured its pensions.
In an interview with BBC Scotland, Iain Gray said the service had to modernise.
The UK Government has argued that the rise of e-mail means the business would never be profitable in its current form.
With a Labour backbench revolt looming on the issue, critics of the proposal said it would undermine universal mail delivery and threaten thousands of jobs.
Dave Watson's comments, which were met with warm applause from delegates, came in the first address of the three-day conference in Dundee.
However, Mr Gray said: "If this is the way to secure the future of Royal Mail and secure the Royal Mail pension fund, then that's something I would be able to support."