NEW YORK — An increased number of shoppers are turning to the Internet this holiday season, and initial reports are that they are responding to promotions and spending more.

According to Coremetrics, a research firm that tracks online sales, Internet shoppers spent 20% more on the Monday after Thanksgiving — the shopping day known as Cyber Monday — than in 2009.

For its part, drugstore.com inc. says the number of customer orders placed through its web sites set a new one-day record.

“We’re focused on offering customers the best selection of products, convenience and great value year-round, and the holidays are no exception,” chairman and chief executive officer Dawn Lepore says.

“This time of year we expand our health and beauty assortment to include a wide selection of fun-to-find gifts, toys and games, gadgets and stocking stuffers that customers want,” she notes. “In addition to this, our Cyber Deals seemed to strike a chord.”

Data released by other retailers indicates that consumers did not wait until Cyber Monday to start their online shopping excursions.

Walmart, for instance, reports that traffic on its walmart.com web site increased by around 30% on the Friday after Thanksgiving and was up by nearly 50% on Thanksgiving Day.

Industry watchers say that getting an early start to the holidays was not uncommon.

“We saw a lot of companies jumping the gun by doing a Thursday-only sale,” Charlie Graham, founder and chief executive officer of ShopItToMe.com, a personal shopping site that works with more than 200 retailers, recently told The New York Times.