NEW YORK — The NFL and its on-field officials’ union failed to reach an agreement when they met Saturday morning, making it more likely replacement officials will work the league’s first week of regular-season games.

Michael Arnold, lead negotiator for the NFL Referees Association, says the union remains “willing to negotiate with the NFL in order to reach a fair agreement.” But Arnold says “no additional meetings are scheduled at this time.”

The league locked out the referees in early June, then hired replacements, whose work in exhibition games has been heavily criticized.

In 2001, the NFL used replacements for the first week of the regular season before a contract was finalized. 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.