AT&T Inc. (NYSE:T), the No. 1 telecommunications carrier, reported first-quarter earnings and revenue rose solidly, ahead of estimates, as smartphone customers spent more time on the network.

As a result, net income rose nearly 6 percent, to $3.6 billion, or 60 cents a share, as revenue inched up 1.8 percent to $31.8 billion, compared with the year-earlier's net income of $3.4 billion, or 57 cents a share, on revenue of $3.4 billion.

The No. 1 wireless carrier reported record sales of smartphones  -- 5.5 million -- including 4.3 million new iPhones from Apple Inc. (Nasdaq: AAPL), the world's most valuable technology company.

Results for the Dallas-based carrier were helped by share buybacks, the collapse of its ill-fated move to acquire T-Mobile USA from Deutsche Telekom, announced a year ago, and lower wireless turnover. The results beat analyst estimates by 3 cents.

We continue to capitalize on our terrific momentum on mobile Internet, said CEO Randall Stephenson. These results add confidence in our outlook for the current year.

AT&T said it now has 103.9 million wireless customers, beating No. 1 Verizon Wireless, controlled by Verizon Communications Inc. (NYSE: VZ), which reported 93 million customers as of March 31.

Still, AT&T reported gaining only 187,000 new customers on contracts for the quarter, mainly for tablets like the iPad, whereas Verizon Wireless last week reported adding 501,100 new customers.

AT&T said one reason for higher profitability was its average monthly revenue per customer was $64.46, a nearly 2 percent gain, reflecting more time engaged with smartphones and tablets on the network. That was considerably higher than Verizon Wireless's average, which was $55.43.

Meanwhile, AT&T also reported progress in its wireline business as well as its data transmission sector, where traffic surged 19 percent over the year-earlier period. AT&T partners in data telecommunications with International Business Machines Corp. (NYSE: IBM).

AT&T reported cash and equivalents fell to $2.4 billion from $3.2 billion on Dec. 31, reflecting cash used for share buybacks.

Stephenson and other AT&T officials are scheduled to brief investors later Tuesday.

AT&T shares opened  at. $31.16, up 55 cents.  So far in 2012, they've risen 1 percent.