NEW YORK — After a strong start to the holiday shopping season, sales at stores have fallen for the third consecutive week as Americans continue to hold back on spending during what is traditionally the busiest buying period of the year.
Sales at US stores dropped 3.1 percent to $42.7 billion for the week that ended on Sunday compared with the same week last year, according to ShopperTrak, which tracks data at 40,000 locations.
That follows a decline of 2.9 percent and 0.8 percent during the first and second weeks of the month, respectively.
The numbers, which don’t include online sales, are another challenge in what has largely been a disappointing holiday shopping season for stores.
The two-month period that begins on Nov. 1 is important for retailers because they can make up to 40 percent of their annual sales during that time.
Retailers started the season cautiously optimistic. But after a strong start through most of November — ShopperTrak said sales were up 3.4 percent for the month — stores have found it increasingly hard to attract shoppers into stores despite big discounts and expanded hours during the final days.
‘‘It’s been a mediocre December,’’ said Bill Martin, cofounder of ShopperTrak.
At the Garden State Plaza Mall in Paramus, N.J., on Saturday, Abercrombie & Fitch, AnnTaylor, and Express had 50 percent off sales, while Aeropostale was discounting its entire assortment up to 70 percent off prices.
Still, shoppers were cautious.
Barbara Jackson, 45, was one of them.
She said she is capping her holiday budget at $1,500 — half of what she spent last year.
That is because Jackson, an aide to the elderly, is earning less than she earned last year. ‘‘I am more budget conscious,’’ Jackson said.
ShopperTrak estimates that holiday sales at stores so far are up 2 percent to $218.4 billion compared with the same period last year.
That is below the 2.4 percent forecast for the two-month period, but the company is standing by that estimate with a few days left before Christmas and a little over a week before the season end.
The National Retail Federation, the nation’s largest retail group, also said it is still standing by its forecast that sales in stores and online combined will be up 3.9 percent to $602.1 billion.
Online spending from home and work desktop computers in the United States from Nov. 1 through Dec. 15 was up 9 percent from the same period last year to $37.8 billion, according to the most available data from comScore.
That is below the 14 percent growth the Internet research firm is forecasting for the season.
But comScore still expects online sales to grow at the pace for the season, but the category accounts for only about 11 percent of spending in the three months that include the holiday shopping season.