"The largest single-employer strike in American history now appears inevitable," Teamsters General President Sean O'Brien said in a statement.

"Executives at UPS, some of whom get tens of millions of dollars a year, do not care about the hundreds of thousands of American workers who make this company run," O'Brien said.

UPS Teamsters have 340,000 members. The union has been locked in negotiations with UPS since mid-April. Earlier this month, it called a strike in the event the company refuses to negotiate a fair agreement before the current five-year contract expires on July 31.