The meeting took place in the presence of Labour Department officials along with representatives of NLC and Unions went on for several hours failed to break the impasse.
The workers have been pressing for various demands, including regularisation of services and wage revision.
According to officials of Jeeva Thozhilalargal Sangam, one of the largest unions that is spearheading the strike, the contract workers would meet the CM tomorrow, hoping to end the strike.
Recently, the Unions and top officials of NLC, including its Chairman and Managing Director Surendar Mohan had held lengthy discussions here to end the strike but it failed.
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Shanmugam, leader of Labour Progressive Front had then said that the unions staged a walkout as the management offered an increase of Rs 100 per day per labourer, to which they were told it was not acceptable.
However, NLC's General Manager, Balaji said the management has made the best offer for the workers.