Environment Minister Zoltan Illes told the BBC the clean-up would take at least one year and probably require technical and financial assistance from the European Union.
An alert has been declared for the Marcal and Torna rivers, and Mr Illes said workers were "desperately" trying to stop contamination of the Raba and Danube rivers.
Hungarian media quoted Mr Illes as saying that a 25-metre-long crack in the weakened wall of the reservoir near Ajka had widened slightly by Sunday morning and that the wall of the damaged reservoir now looked beyond repair.