UPS Inc. has made a contract offer to the Teamsters union that the union said Friday represents “significant movement” on wages, benefits and worker classification language.

The company has also pledged to have a deal done by Wednesday to cover 340,000 Teamster employees, the union said.

Despite the progress, it isn’t enough, the union said in a statement. After UPS executives left the negotiating room, Teamster national committee members caucused and agreed to continue to put pressure on the company. “One of two things is going to happen next-UPS will come to terms on a deal we can confidently recommend to our members, or UPS will fail and the company will put itself on the street,” said Fred Zuckerman, the Teamsters general secretary-treasurer.

“At every step, we are forcing (UPS) to do what they don’t want to do, which is to give our members more money and better protections at work,” said Teamsters General President Sean O’Brien. “UPS didn’t want to make progress on economics, but they conceded today that they will reach a deal by July 5 because they have no choice.”

The news comes two days after the Teamsters demanded that UPS present its “last, best and final offer” on the economic language of the contract. Such a demand is not binding on either side or on the bargaining process. Typically, it is a negotiating tactic used by one side to exercise leverage over the other.

The current contract expires at 11:59 p.m. ET on July 31. The Teamsters have warned repeatedly that they will strike Aug. 1 without a contract in place.

“We are encouraged the Teamsters are ready to continue negotiations and discuss our most recent proposal,” UPS said in a statement. “Productive discussions are critical at this stage of the process. We look forward to the union’s input so we can reach a timely agreement and provide certainty for our employees, our customers and the U.S. economy.”

The Teamsters will hold a press conference Saturday at noon ET outside Teamsters headquarters.