Contract negotiations between UPS Inc. and the Teamsters union collapsed early Wednesday morning, with each side blaming the other for its demise.

The Teamsters issued a statement saying that UPS (NYSE: UPS) walked away from the bargaining table at 4 a.m. after presenting an unacceptable offer to the Teamsters that did not address members’ needs. The UPS Teamsters National Negotiating Committee unanimously rejected the package.

Following marathon negotiations, UPS refused to give the Teamsters a last, best and final offer, telling the union the company had nothing more to give, the Teamsters’ statement said.

“This multibillion-dollar corporation has plenty to give American workers — they just don’t want to,” said Teamsters General President Sean M. O’Brien. “UPS had a choice to make, and they have clearly chosen to go down the wrong road.”

The five-year UPS Teamsters contract covering more than 340,000 full- and part-time workers expires July 31. No additional negotiations are scheduled, the Teamsters said. The union has threatened to strike Aug. 1 without a contract in-hand. The rank-and-file has overwhelmingly authorized a strike should talks break off.

In its statement, UPS said the Teamsters have “stopped negotiating despite UPS’ historic offer that builds on our industry-leading pay. We have nearly a month left to negotiate. We have not walked away, and the union has a responsibility to remain at the table.

“Refusing to negotiate, especially when the finish line is in sight, creates significant unease among employees and customers and threatens to disrupt the U.S. economy. Only our non-union competitors benefit from the Teamsters’ actions,” UPS said.

The company said that “we’re proud of our offer. It delivers wins for our people. The Teamsters should return to the table to finalize this deal.”

Over the weekend, UPS agreed to end a two-tier driver pay system and convert all junior drivers into regular package car drivers with the same pay as their senior counterparts. UPS also agreed to establish Martin Luther King Day as a paid holiday.