SAN FRANCISCO — Facebook is betting that one day soon, we’ll all be acting like high school students — more texting and instant-messaging, at the expense of e-mail.

Facebook has unveiled a new messaging system, and while CEO Mark Zuckerberg didn’t go as far as declaring e-mail dead, he clearly sees the four-decade-old technology being eclipsed by more real-time ways of communicating.

“We don’t think a modern messaging system is going to be e-mail,” Zuckerberg said.

Right now, Facebook’s Messages section is a lot like an e-mail inbox. The overhauled version, which will be rolled out to users by invitation in coming months, brings in cell phone texts, IM chats and e-mails from non-Facebook accounts.

All the messages stack up in one inbox, and they’re organized by the person sending them rather than the type of technology they use. For those who want one, Facebook will hand out facebook.com e-mail addresses — mostly to make it easier to communicate with people who aren’t on Facebook.

“If we do a good job, some people will say this is the way that the future will work,” Zuckerberg said.

By making e-mail part of its communications hub, Facebook escalates its duel with Internet search leader Google Inc., which shook up online communications 6½ years ago with its Gmail service. Google has said it will roll out more social networking features to counter Facebook’s growing popularity, and within Gmail it already lets people chat, e-mail and make phone calls.

Yahoo, AOL and Microsoft are also working on incorporating messages from Facebook, Twitter and other social sites into their main e-mail systems.

What Facebook has that Gmail doesn’t have, however, is people’s real identities, plus a map of their real-life relationships and online interactions — something Facebook likes to refer to as the “social graph.”

Facebook will use what it knows of these relationships to build a social inbox that not only filters out spam but messages it deems less important from strangers or overly chatty friends, and impersonal messages such as the phone bill. Those lower-priority messages will be tossed in a separate folder labeled “Other.” Users can also limit who can send them messages to their Facebook friends, and Facebook will toss out the rest.

To communicate with a friend, a Facebook user would click on the friend’s name rather than hunt for a phone number or an e-mail address. If that friend prefers to get text messages, that’s how the message will be seen. If the friend likes e-mail, e-mail it will be.

The messaging system, however, isn’t e-mail. It doesn’t use subject lines or “Cc” fields.

Facebook says it will store every message sent between two people for eternity, unless they choose to delete it; the company likens it to this generation’s equivalent of a box filled with years of love letters.