Bank branches are continuing to lose their luster as consumers rely on online and mobile channels, according to a new report.

In its report, "Banking Shaped by the Customer," Accenture said that 81% of consumers would stick with their bank even if their local branch closed, compared to 52% in 2013. A third of consumers said that online banking was the most important channel for banks to focus on in the next five years; 20% of participants pointed to mobile banking.

"For the first time in our research, consumers ranked online banking services as the number one reason for staying with their bank," Robert Mulhall, a managing director at Accenture, said in a press release Tuesday. "It's no longer a question of proximity to the local branch that is driving consumer choice, it's a matter of which banks are offering the strongest online capabilities and mobile applications."

The report strongly emphasized a focus on millennials, who Mulhall said were "becoming one of the most influential ... customer groups" for banks as they begin to surpass baby boomers as the nation's largest living generation.

While 92% of millennial respondents said they were satisfied with the online banking experience at their primary bank, nearly a fifth said they had switched primary banks in the past year.

Millennials also had strong preferences for the types of services they want; 47% want banks to provide tools to create and monitor a budget, while nearly half want the option to video chat with a banking representative.

"Not only are millennials more likely to switch banks, but many continue to migrate to online-only banks, which poses a significant risk for banks in the future," Mulhall said.

Unexpectedly, millennials are not leading the online charge. Accenture found that 31% of consumers between 35 and 39 had switched to an online-only bank in the past year, compared to 17% of millennials.

Still, in any event, banks need not worry about losing the trust of consumers, especially when it comes to managing data. Nearly 90% of participants said they had the most confidence in banks and financial institutions to handle their data, compared to 7% selecting payment companies.

Accenture surveyed around 4,000 bank customers in North America for its report, with 70% of respondents located in the United States.