The move follows Asda's decision last week to cut the prices of selected vitamins and minerals by up to 20 per cent.
The warning came as Tesco threatened to shake up the newspaper and magazine distribution industry and spark a price war.
Tesco claims the system controlling the supply of newspapers and periodicals is restrictive and outdated. Asda is also considering mounting a challenge.
The three companies that have threatened to serve injunctions on Asda are Procter & Gamble, Warner Wellcome and Reckitt & Colman, whose brands include Lemsip. As Asda is not currently discounting any of their products, the action is seen as an attempt to prevent any extension of the price- cutting.
Asda said: "We will vigorously defend these injunctions. We never suggested any further price cuts but we are opposed to resale price maintenance. Our discounts have proved popular with our customers."
Asda said it welcomed the announcement from the Office of Fair Trading last week that it was reviewing the system that allows pharmaceutical manufacturers to set the prices of their products.
Asda shares rose 0.5p to 97p.
However, shares in Sainsbury fell 2p to a 10-month low of 408p on price- war concerns and City fears that it is still losing market share to Tesco.
Tesco said yesterday it was prepared to set up its own distribution network for newspapers and magazines if it could not agree changes with wholesale suppliers such as WH Smith and John Menzies.
The company claims the current system is structured for the benefit of small, local newsagents rather than volume suppliers.
WH Smith rejected the criticisms and said that the OFT and the Monopolies and Mergers Commission had already investigated the supply system.
But its shares slumped 12p to 375p on fears that a challenge from the supermarkets would wipe out a significant proportion of its profits.
Tony Shiret, retail analyst at BZW said: "If Tesco can get supplies direct from publishers it will be able to cut costs and discount magazine prices."
Last year Smiths made pounds 37m of its pounds 112m profits from the supply of newspapers and magazines.