P&G’s organic sales, a closely watched metric that strips out deals and currency moves, rose 7% for the year ended June 30, the most since 2006. Shoppers paid substantially higher prices.

But consumers are beginning to cut back amid mounting inflation, executives said. They are using up products they stockpiled during the pandemic or holding off on replenishing supplies. Sales volumes declined 1% in the most recent quarter.

“For us, the downturn is not yet visible,” P&G finance chief

Andre Schulten

said. “We’re also not naive, we see the pressure on the consumer.”

P&G expects organic sales growth of 3% to 5% for the current year, the lowest since 2019 when the company notched a 5% increase. The company predicts consumer-goods industry growth will slow by a percentage point or more from the last fiscal year’s 5% growth.

P&G Chief Executive

Jon Moeller

said in an interview that consumers are beginning to shift to cheaper, private-label alternatives, a trend already under way in food and beverages. He called the shift small but noticeable.

Mr. Moeller said he is confident that growth, though more muted relative to the past few years, will remain solid as high employment levels coupled with healthy household balance sheets enable consumers to keep spending on necessities while they cut costs elsewhere.

“There is no inherent reason why people are just going to stop buying modestly priced consumer products, daily-use essentials where performance matters,” he said. “You have to look elsewhere to get signals of consumer stress.”

P&G shares fell more than 6%.

P&G’s results and outlook largely echo the messages coming from other big consumer brands. Companies including

Coca-Cola Co.

,

McDonald’s Corp.

and

Kimberly-Clark Corp.

this week reported sales gains driven by higher prices, and executives said they would keep passing along increased costs to shoppers for now. Yet some executives also said consumers are starting to show signs of stress, trading down to cheaper brands or cutting back on how much they buy.

The world’s biggest consumer packaged goods company by sales, P&G has largely outpaced competitors amid the pandemic, especially in the U.S.

Rivals are showing signs of gaining ground.

Colgate-Palmolive Co.

on Friday said it now expects bigger-than-expected organic sales gains, predicting an increase of 5% to 7% for the calendar year, up from 4% to 6%. Last week,

Kimberly-Clark

and

Unilever

PLC also raised sales outlooks for the calendar year.

Church & Dwight Co.

Chief Executive

Matthew Farrell

said on Friday that demand is accelerating for low-cost laundry detergent, while people are giving up electric toothbrushes for manual options. “Consumers are making choices to make their budget stretch further,” he said.

A central question is how consumers and retailers respond to further price increases. P&G said Friday that it had announced to retailers another round of price increases, in mid-single-digit percentages, which will take effect toward the end of summer.

P&G, after more than four years of market-share gains, lost share in the four-week period ended July 16 compared with a year ago, Bernstein analyst Callum Elliott said in a research note analyzing retail data. Losses are in every category except for beauty, he said.

“While prices spiral, the consumer also continues to adjust to the new reality,” he said.

Mr. Moeller said P&G continues to gain market share broadly in the U.S. and globally.

Organic sales rose 7% in the quarter ended June 30, with prices up 8% on average. P&G attributed the 1% decline in sales volume primarily to Covid-related shutdowns in China and intentional downsizing of its business in Russia amid the war in Ukraine.

P&G reported $19.5 billion in revenue for the quarter, up 3% from a year ago. Diluted net earnings per share were $1.21, up 7%.

The company expects diluted net earnings per share will be between flat and up 4% for the fiscal year as it faces an anticipated $3.3 billion hit tied to foreign-exchange rates and higher costs for materials and freight.

Write to Sharon Terlep at sharon.terlep@wsj.com