"The cigarette factories are commencing production progressively," ITC said in a BSE filing.
On May 5, ITC had said it has shut down its production till the time it is able to comply with "interim requirements" of 85 per cent pictorial warnings.
On May 4, the Supreme Court had directed tobacco companies to implement the rule mandating larger pictorial warnings and refused the manufacturers' plea to stay the implementation of new cigarette packaging rules introduced from April 1.
"In the meantime, the company has had to shut its cigarette factories from May 4, 2016, until the company is in a position to comply with the interim requirements pending hearing in the Karnataka High Court," ITC had said in a BSE filing on May 5.
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Last month, the company had resumed manufacturing of cigarettes at its factories, which it had suspended from April 1, in protest against the larger pictorial warnings issue.
A notification by the Health Ministry on September 24, 2015, for implementation of the Cigarettes and other Tobacco Products (Packaging and Labeling) Amendment Rules, 2014, had come into force on April 1, 2016.
It prescribed larger pictorial warnings, covering 85 per cent of packets on tobacco products.
ITC manufactures a range of brands, including India Kings, Classic, Gold Flake, Navy Cut, Capstan, Bristol, Flake, Silk Cut, which are manufactured at plants in Bengaluru, Munger, Saharanpur, Kolkata and Pune.