NEW YORK – BlackBerry users across the world were exasperated Wednesday as an outage of email, messaging and Internet services on the phones spread to the U.S. and Canada and stretched into the third day for Europe, Asia, Latin America and Africa.

It was the biggest outage in years for BlackBerry users, and strained their relationship with an already tarnished brand. It came on the eve of the launch of a mighty competitor — a new iPhone model.

Research In Motion Ltd., the Canadian company that makes the phones, said a crucial link in its European infrastructure failed Monday, and a backup didn’t work either. The underlying problem has been fixed, but a backlog of emails and messages has built up that the company has yet to work down.

Meanwhile, emails and messages from other regions to Europe were piling up in RIM’s systems in the rest of the world, like letters clogging a mailbox. That caused the outages in the U.S. and Asia, said David Yach, RIM’s chief technology officer for software.

At Zenprise Inc., a Fremont, Calif., firm that helps companies manage BlackBerrys issued to employees, vice president Ahmed Datoo said emails started piling up on U.S. servers shortly after midnight. By morning, the congestion was heavy enough at a particular client company to delay all email for BlackBerrys. The pileup started to ease in the afternoon.

RIM is already struggling with delays in getting new phones out, a tablet that’s been a dud and shares that are approaching a five-year low. In the latest quarter, it sold 10.6 million phones, down from 12.1 million the same period last year.

The duration of the latest outage could force large businesses to rethink their use of BlackBerrys, said Gartner analyst Carolina Milanesi. Many of them have stuck with the phones because of the quality and efficiency of its email system, but that’s now in question, she said.

Consumers are having second thoughts too. Andrew Mills, a child abuse investigator for the state of Arkansas, said he’d been thinking of getting some other smartphone for a while, and the outage was the “nail in the coffin” for him.

The 27-year-old has used BlackBerrys for five years, but friends and family have abandoned them, and he’s set to do so in a few weeks. “From what I can see on their new phones they’re not doing anything that’s competing with Droid and iPhone,” he said.

In the United Arab Emirates, the two biggest phone companies said they would compensate their BlackBerry users for the mishap by giving them at least three days of free service. Matthew Willsher, chief marketing officer for Etisalat, the country’s biggest telecom, said it was acting in response to the “exceptional and unprecedented circumstances.”

Unlike other cellphone makers, RIM handles email and messaging traffic to and from its phones. That allows it to provide services that other phones don’t have, optimize data service and provide top-class security. But when it encounters a problem, a large share of the 70 million BlackBerry subscribers worldwide can be affected all at once. BlackBerry outages tend to occur several times a year, but they usually last for less than a day.

One of the BlackBerry’s big attractions is the BlackBerry Messenger, or BBM, which works like text messaging but doesn’t incur extra fees. That service was affected by the outage, and to make matters worse for RIM, Apple Inc. was releasing software Wednesday for its iPhones that works like BBM. The iPhone 4S will be released on Friday. Competition from Apple is one of the chief causes of RIM’s diminishing fortunes.

RIM shares fell 53 cents, or 2.2 percent, to close New York trading at $23.88 as major indexes rose. The shares hit $19.29 a week ago, the lowest since 2006.