Bill Morris, leader of the Transport and General Workers Union, urged Labour to commit itself to a statutory rate of pounds 4 an hour, but Bill Jordan, president of the AEEU engineering union, said such an argument was irresponsible.
The public disagreement sets the scene for a battle within the Labour Party during the next election.
Speaking at the Scottish TUC, Mr Morris said action was needed to tackle poverty wages so that the state did not subsidise employers by paying their workers benefits.
During the 1992 election campaign, Labour watered down its initial commitment to a national minimum wage of pounds 3.40 an hour. Mr Morris said: 'Labour must plan now to win social justice. That means a firm commitment to universal benefits and the restoration of the link between pensions and average earnings.'
However in Llandudno, at his union's annual conference, Mr Jordan said that any attempt to put a figure now on a statutory minimum would hand the Tories a propaganda weapon.
It was irresponsible when not in government to dictate the level of a minimum wage.
Mr Jordan said the union was increasing its membership because of legislation forcing unions to gain written authority from members before subscriptions are directly deducted from their wages.