NEW YORK — BlackBerry users across the world were exasperated Wednesday as an outage of e-mail, 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 competitor, a new iPhone model.

Research In Motion, 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 e-mails and messages has built up that the company has yet to work down.

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