In high-stakes labor contract negotiations between Sandy Springs-based UPS and the International Brotherhood of Teamsters, the union is now targeting a path toward a contract deal well ahead of a strike deadline.

The Teamsters said the company’s management has agreed to put a contract offer on the table by Wednesday July 5. That would allow enough time to vote and approve an agreement before the union’s Aug. 1 strike deadline.

On Saturday, the Teamsters said negotiators had reached tentative agreements with UPS to resolve some key issues, including ending a two-tier pay system, stopping required overtime on a day they aren’t scheduled to work and establishing Martin Luther King Jr. Day as a full holiday.

The Teamsters labor contract extends through July 31. It is the nation’s largest private-sector collective bargaining agreement, covering some 340,000 UPS workers, including drivers and package handlers. The union has threatened to strike Aug. 1 if it did not have a new contract agreement by that time.

Both sides could benefit from an early deal. UPS CEO Carol Tomé told investors early this year before the start of negotiations that “we are not far apart on the issues,” and said she was “committed to delivering with the rest of the team a win-win-win contract before the end of July.”

Meanwhile as the talks continue and the Teamsters ratcheted up pressure on the company with their threat of a potential strike, UPS has been losing some business to competitors, including FedEx, as customers worry about how they would move their goods if there is a strike.

By reaching a deal early and averting a strike threat, UPS could better stem the loss of business and attract new business.

Tomé also said in April that the company had a pipeline of potential business worth more than $6 billion, but that it was “hard to sell into... because of that Teamsters negotiation.”

“But we are going to go hard at it once we have that handshake deal,” Tomé said. “We’ve got to win faster, and we will win faster when the uncertainty is behind us” of the Teamsters negotiations.

“We’re aligned,” she said in April. For example, Tomé acknowledged the Teamsters wanted to end required six-day work weeks for some workers, and that she agreed that “we shouldn’t force you” to work six days a week.

On Friday, the company issued a statement saying it is “encouraged the Teamsters are ready to continue negotiations and discuss our most recent proposal.”

”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 company said.

The union last Wednesday issued a statement saying it had asked for a last, best and final offer from the company by Friday — a month ahead of the strike deadline. However, late Friday the union said it would continue negotiating, after saying the company came back with a revised counterproposal “with significant movement on wages and other economic language.”

“We’ve gotten some changes that are better” for members, said Teamsters General President Sean O’Brien in a press conference on Saturday. “But we’re not there yet.

“UPS came back to the table knowing we were serious, made some movement. So we made a commitment to resume negotiations,” O’Brien said.

The two sides now appear to be on a path to have a deal both agreed to and approved by members by the Aug. 1 deadline.

“We have to come to an agreement by July 5 in order to get that thing ratified by the expiration date,” O’Brien said.

The union has also outlined a series of agreements reached in negotiations that would benefit members — but only if a contract is approved.

While O’Brien has a reputation for a militant stance and tough-talking approach, he also sounded some optimistic tones amid negotiations about what the UPS contract could accomplish for the union’s goals.

“We’re going to use this contract to help change the lives of people that are in this industry non union,” including non-union Amazon workers, O’Brien said. “We’re going to take this contract and say ‘this is what you’re gonna get when you join the Teamsters union.’ ”

“We want to leverage our power,” O’Brien said. “This is going to be the defining moment not only for the Teamsters union, but also organized labor throughout this country.”