Pilkington said the 158p-a-share written proposal from Japanese firm Nippon Sheet Glass was too low even though it represented an improvement on the £1.97 billion approach last month.
It said: 'The board of Pilkington has considered the revised proposal and has informed Nippon that the pre-conditions are unacceptable and the price still falls short of a level which it would be prepared to recommend.'
Nippon owns nearly 20 per cent of Pilkington and analysts believe the company could generate savings from combining its UK subsidiary NGF Europe with the headquarters of Pilkington as they are both based in St Helens.
A price of around £2 billion on Pilkington puts it in line with the recent take-overs of Aggregate Industries, RMC and Novar.
But traders see growing opportunities in selling glass as a commodity, particularly to the construction sector.
Shares in Pilkington have more than doubled over the past two years on bid speculation and an improving operational performance, which was underlined last month by a 22 per cent hike in first-half profits to £99 million despite rising energy costs.
Pilkington employs approximately 24,000 people and has plants in Birmingham and Doncaster. It has sales and distribution operations in more than 130 countries.