Nationalised and under special administration, Ilva's main facility at Taranto in southern Italy is notorious as one of the most polluting industrial facilities in Europe but also an economic lifeline in a region blighted by high unemployment.
Two consortiums have put forward rescue plans with global steel giant ArcelorMittal's partnership with Italy's Marcegaglia said to be favoured by the administrators over a rival team including Indian group Jindal South West Steel, Italian specialist steelmaker Arvedi, the Italian state's CDP investment bank and Delfin, the holding company of Italian businessman Leonardo Del Vecchio.
Union boss Maurizio Landini said the plans were unacceptable.
"The meeting was disappointing ... We don't even understand why one offer has been preferred over the other," he said.
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Further talks with unions are scheduled for Thursday before Economic Development minister Carlo Calenda makes a decision.
ArcelorMittal has promised to invest 2.3 billion euros into Ilva in addition to a reported purchase price of early two billion euros.