The two sides failed to reach an agreement Saturday when they met for the third day in a row, and the league said it's proceeding with replacement officials.
The NFL locked out the referees in early June, and hired replacements, whose work in exhibition games has been heavily criticized.
On Sunday, it sent teams a memo saying it upped its offer to the union and thought it was close to a deal, but the union says "there was no agreement ... to do anything other than to meet on Saturday. Any claim that numbers were agreed to before Saturday is absolutely false."
The NFL's memo says it offered more money in order to reach a deal before the regular season started, and thought the union was planning to reach one on Saturday.
In a memo obtained by The Associated Press, the NFL said that on Saturday "the officials immediately did an about-face and made clear that they had no intention of settling within the agreed-upon parameters."
The union says that "after locking out the NFL Officials on June 3 and refusing to negotiate with the NFLRA, the NFL is now engaged in a misinformation campaign."
The statement goes on to say "there was no agreement on Thursday or Friday to do anything other than to meet on Saturday. Any claim that any numbers were agreed to before Saturday is absolutely false."
The NFL has seen and heard the problems the replacements have had this summer, something that tests the integrity of the sport. The speed of the game and the amount of time starters are on the field increase exponentially for real games, making the replacements' task more challenging.
In 2001, the NFL used replacements for the first week of the regular season before a contract was finalized.
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