June 26 (Reuters) - Fast-food chain Taco John's and New Jersey-based Gregory's Restaurant & Bar urged the U.S. Trademark Office on Friday to reject petitions by Taco Bell (YUM.N) to cancel their federal trademarks covering the phrase "Taco Tuesday."

Taco Bell had publicized its effort as a bid to "liberate" the phrase for restaurant owners. But Wyoming-based Taco John's, which owns trademark rights to "Taco Tuesday" across most of the United States, said Taco Bell's only interest was to sell more of its own tacos.

Gregory's Restaurant also denied Taco Bell's claim that it was not entitled to its "Taco Tuesday" trademark rights covering the state of New Jersey.

Taco Bell said in a statement on Monday that it "affirms its position that Taco Tuesday is a generic term, not a trademark."

Taco John's said in a statement on Monday that the company would "let the process continue."

An attorney for Gregory's Restaurant did not immediately respond to a request for comment on Monday.

Yum Brands Inc's Taco Bell, the largest Mexican fast-food chain in the U.S., asked the trademark office in May to cancel its smaller competitors' "Taco Tuesday" trademark registrations, accusing them of wrongly monopolizing the use of a generic phrase in the restaurant industry.

"Nobody should have exclusive rights in a common phrase," the petitions said. "Can you imagine if we weren’t allowed to say 'what's up' or 'brunch'? Chaos."

Taco John's noted on Friday that it has held its federal trademark for 34 years. It rejected the argument that the phrase "Taco Tuesday" is too common to warrant trademark protection and said its trademark "does not prohibit petitioner or anyone from advertising and selling tacos on Tuesday."

The cases are Taco Bell IP Holder LLC v. Spicy Seasonings LLC, U.S. Trademark Office, No. 92082333 and Taco Bell IP Holder LLC v. Gregory Hotel Inc, U.S. Trademark Office, No. 92082327.

For Taco Bell: Alexandra Bistline of Pirkey Barber

For Taco John's: Harold Bruno of Robinson Waters & Odorisio

For Gregory's Restaurant: Stephen Altamuro of Law Offices of Stephen Altamuro