On perhaps the busiest online shopping day of the year, the Supreme Court refused to wade into a dispute about state sales taxes for purchases on websites like Amazon.com, an outcome likely to prompt more states to attempt to collect taxes on Internet sales.

Monday’s court action means “it might be the last Cyber Monday without sales tax,” said Joseph Henchman of the Washington-based Tax Foundation.

It’s all part of a furious battle — also including legislation in Congress — among Internet sellers, millions of buyers, aggrieved brick-and-mortar stores and states hungry for billions of dollars in extra tax revenue.

The high court without comment turned away appeals from Amazon.com LLC and Overstock.com Inc. in their fight against a New York court decision forcing them to remit sales tax the same way in-state businesses do. This could hurt online shopping in that state, because one of the attractions of Internet purchasing is the lack of a state sales tax, which makes some items a little cheaper than they would be inside a store on the corner.

And the effect could be felt far beyond New York if it encourages other states to act. The National Council of State Legislatures estimates that states lost an estimated $23.3 billion in 2012 as a result of being unable to collect sales tax on online and catalog purchases.

The court’s refusal “allows states that have passed laws like New York’s to continue doing what they’ve been doing,” said Neal Osten, director of the Council’s Washington office.

Web retailers generally have not had to charge sales taxes in states where they lack a store or some other physical presence. But New York and other states say that a retailer has a physical presence when it uses affiliates — people and businesses that refer customers to the retailer’s website and collect a commission on sales. These affiliates range from one-person blogs promoting the latest gadgets to companies that run coupon and deal sites.

Amazon and Overstock both use affiliate programs. Amazon has been collecting sales tax in New York, even as it fights the state over a 2008 law that was the first to consider local affiliates enough of an in-state presence to require sales tax collection. Overstock ended its affiliate program in New York in 2008 after the law passed and has ended its affiliate programs in other states that have tried to force it to collect sales taxes.

Without the affiliate programs, companies still can sell in those states but just won’t partner with local people and businesses that refer customers to their sites.

Both companies collect sales taxes in some states. For example, Overstock.com collects taxes in Utah, where it is based. Amazon says it collects sales tax in 16 states.

“Today’s Supreme Court decision validates New York’s efforts to treat both online and brick-and-mortar retailers equally and fairly, by requiring all retailers with a presence in our state to collect sales taxes,” New York Attorney General Eric T. Schneiderman said.

But each state has its own rules. While Monday’s result settles the issue for New York, legislatures and courts in other states have come to different conclusions — meaning that some Americans will still get state tax-free Internet purchases from certain websites, while others won’t simply because of where they live.

In October, for example, the Illinois Supreme Court threw out a law that would tax certain Internet sales, saying the “Amazon tax” violated federal rules against discriminatory taxes on digital transactions. State officials are considering whether to appeal their case to the U.S. Supreme Court.