The International Brotherhood of Teamsters union is ratcheting up pressure on Sandy Springs-based UPS in labor contract negotiations, with threats of a strike Aug. 1 if the two sides don’t reach agreement.

The Teamsters said their negotiators walked away from the bargaining table Wednesday and are demanding a last, best and final offer from the shipping giant by this Friday.

UPS said it submitted a proposal last week, and this week submitted a “significantly amended proposal to address key demands from the Teamsters.”

“We’re working around the clock to reach an agreement that strengthens our industry-leading pay and benefits ahead of the current contract’s expiration on August 1,” UPS said in a written statement. “We remain at the table ready to negotiate.”

But the Teamsters said UPS’s counter-proposal offered “miniscule raises and wage cuts to traditional cost-of-living adjustments.”

With the union demanding another proposal by this Friday, the Teamsters said UPS “risks putting itself on strike by August 1 and causing devastating disruptions to the supply chain in the U.S. and other parts of the world.” Teamsters General President Sean O’Brien said in a written statement: “The largest single-employer strike in American history now appears inevitable.”

Teamsters members earlier this month voted to authorize a strike if the two sides do not reach agreement on a new contract. That does not mean a strike will happen, but is a common negotiating tactic by unions.

“Come August 1, it’s going to be damn hard for UPS to ignore us any longer,” said Teamsters General Secretary-Treasurer Fred Zuckerman in a written statement on Wednesday.

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