The head of the Teamsters union said Sunday that he has asked the White House not to intervene if unionized UPS workers end up going on strike.

Negotiations between the delivery company and the union representing 340,000 of its workers have been at a standstill for more than a week, with a July 31 deadline for a new contract approaching fast.

The union has threatened a strike if a deal is not reached by the time the collective bargaining agreement expires. Asked during a webcast with members Sunday on whether the White House could force a contract on the union, the president of the Teamsters, Sean O’Brien, said he has asked the White House on numerous occasions to stay away.

“My neighborhood where I grew up in Boston, if two people had a disagreement and you had nothing to do with it – you just kept walking,” Mr. O’Brien said.

“We don’t need anybody getting involved in this fight,” he said.

The Teamsters represent more than half of the Atlanta-based company’s workforce in the largest private-sector contract in North America. If a strike does happen, it would be the first since a 15-day walkout by 185,000 workers crippled the company a quarter century ago.

Before contract talks broke down, both sides had reached tentative agreements on several issues, including installing air conditioning in more trucks and getting rid of a two-tier wage system for drivers who work weekends and earn less money. A sticking point in negotiations is wage increases for part-time workers, who make a minimum of $16.20 an hour, according to UPS.

Last week, UPS said it will temporarily begin training nonunion employees in the United States to step in should there be a strike.