NEW YORK — Starbucks expressed confidence that an overhaul of its rewards program will drive up sales over the long term, but warned the transition could be bumpy.

The company reported disappointing sales growth Thursday for the first three months of the year. Global comparable sales rose 6 percent, including a 7 percent increase in its flagship U.S. market.

While the reward changes went into effect just last week, Starbucks said early signs are encouraging and that customer spending is up across loyalty program members, including those who stood to lose out from the change.

“We are not seeing any of the noise that has been speculated on,” said Matt Ryan, Starbucks’ chief strategy officer, in a call with analysts.

The loyalty program in the U.S. now rewards “stars” based on how much people spend, rather than how often they visit. That means customers who buy a plain $2.50 coffee or other small items now need to spend more to earn a free drink or food item.

The change had prompted worries that angered customers would take their business elsewhere.

Despite the positive early signs, however, Starbucks executives warned that there could be “noise” and “bumpiness” in coming quarters as customers adjust to the change.