The statement came after McCormick upped its bid to 65p a share.
However, Premier said it was willing to open talks with the US company.
Premier, the maker of Mr Kipling cakes and Bisto gravy, revealed last week that it had already rejected two takeover offers from McCormick.
In its latest statement, Premier said it was "prepared for meetings to take place in order to discuss value drivers, a review of material pensions documentation, current trading and material contracts, and so to establish whether McCormick will increase its offer price to a recommendable level".
In afternoon trading, Premier's shares were 6.2% higher on the day at 60p.
McCormick is chiefly known for its Schwartz spices and Lawry's seasonings. It first made a bid of 52p a share last month and then raised it to 60p a share on 14 March.
Also last week, Japanese noodle maker Nissin Foods agreed to buy a 17.27% stake in Premier Foods.
Nissin, which Premier describes as a "long-term shareholder", is expected to take a seat on the Premier board.
Premier used to be one of the UK's biggest food groups, but came unstuck when it expanded too fast, loading itself with debt.
It has since sold off its Hovis bread business to the US-based Gores group, rebuilt its Â£20m production line at its Mr Kipling bakery in Barnsley and pushed through a Â£1.1bn refinancing package, which included a Â£353m rights issue.
It still owns a range of household UK brands, such as Ambrosia rice pudding, Oxo stock cubes and Batchelors soups.
Premier is increasing its international operations following its co-operation deal with Nissin that allows Premier to distribute its products in the UK, while making its own products more widely available in key overseas markets.
Nissin invented the first instant noodles in 1958 and operates in 19 countries. Its products include Cup Noodles and Top Ramen.
UK food manufacturer Premier Foods has turned down a third bid by US spices and herbs maker McCormick, saying it "continues to undervalue" the company and its prospects.