Starbucks said on Monday that it intended to bargain “in good faith” with a Buffalo store where employees voted to unionize this month after a sometimes contentious election campaign.

The store is the only one of roughly 9,000 company-owned locations in the United States to have a union, though many locations owned and operated by other companies under licensing agreements with Starbucks have unions.

“From the beginning, we’ve been clear in our belief that we do not want a union between us as partners, and that conviction has not changed,” Rossann Williams, the company’s president of retail for North America, said in a letter to U.S. employees on Monday.

“However, we have also said that we respect the legal process,” she added. “This means we will bargain in good faith with the union that represents partners in the one Buffalo store that voted in favor of union representation.”

Throughout the campaign in Buffalo, which began in late August, union supporters complained that out-of-town officials who converged on their stores, including Ms. Williams, were monitoring and intimidating them. The company said that the officials had gone to Buffalo to help solve issues like understaffing and inadequate training, and that it had taken similar steps around the country since the spring.

But after the announcement of the results of elections at three Buffalo-area stores on Dec. 9, in which the union won in one store, lost in one and was leading in a third store where vote challenges must still be resolved, the union indicated it wanted to take a more conciliatory posture.

“We’d like to sort of offer the olive branch to the company and say, ‘Let’s put this behind us,’” said Michelle Eisen, a Starbucks employee in Buffalo who was one of the leaders of the organizing campaign. “Now is the time, let’s get to the bargaining table as quickly as possible and help us negotiate the best contract that the service industry has ever seen.”

The union said last week that it had filed an objection to the election at the Buffalo-area location where it lost, arguing that the company’s actions violated the “laboratory conditions” under which elections are supposed to be held, making a fair vote impossible.

Starbucks has invested heavily over the years in its reputation as a good employer. Part-time employees are eligible for health insurance, and the company covers tuition for employees who are admitted to an online degree program at Arizona State University. Starbucks’ annual report details its generosity toward employees and says they are “significant contributors to our success as a global brand that leads with purpose.”

In the days before Ms. Williams’s letter, union supporters said the company was continuing to intimidate and monitor employees at three more Buffalo-area stores that had filed petitions for union elections.

“We’re asking them to drop this anti-union campaign and end this union busting,” Jaz Brisack, an employee who helped lead the union campaign, said in a statement on Friday. “We have to ask, why are abusive out-of-state ‘support’ managers still in our Buffalo community?”

The company denies that it has been trying to intimidate workers and says the out-of-town personnel are helping to resolve operational issues at the stores. An election date has not yet been set at those stores or two Boston-area stores where workers filed for union elections after the Buffalo results this month.