SAN FRANCISCO — Apple Inc., trying to build on the success of its iPhone, is developing two new versions, one of which will work over the Verizon Wireless network, the Wall Street Journal reported.

Mass production of the Verizon Wireless phone is scheduled for September, said the newspaper, which didn't name its sources. The other new iPhone may debut this summer, the Journal said.

AT&T Inc. has been the exclusive U.S. carrier for the iPhone since its debut in 2007, gaining an advantage over rivals in the smartphone market. An agreement with Apple would let Verizon Wireless tap rising demand for the iPhone, which has sold more 42 million units.

The iPhone, which lets users surf the Web, listen to music and watch videos, consumes about twice the bandwidth of other smartphones, according to Sanford C. Bernstein & Co. That's strained AT&T's network, particularly in major cities such as New York and San Francisco, AT&T wireless chief Ralph de la Vega said in December. The company has said it's spending an extra $2 billion this year to help ease capacity crunches.

Jeffrey Nelson, a spokesman for Basking Ridge, New Jersey-based Verizon Wireless, declined to comment.

Mark Siegel, a spokesman for AT&T, which has its headquarters in Dallas, said the company has a "great relationship with Apple." The iPhone will be an important part of the company's lineup for a long time to come, he said.

"Apple doesn't comment on rumor and speculation," said Natalie Kerris, a spokeswoman for the Cupertino, California- based company.

Apple named AT&T as the provider of wireless service for its iPad tablet computer in January. That surprised Allen Weiner, an analyst at Gartner Inc., given AT&T's struggle to handle the heavy usage of the iPhone. Verizon and AT&T are both beginning to offer more kinds of devices, such as low-cost computers, as they seek new ways to keep growing.

Two Taiwanese companies, Hon Hai Precision Industry Co. and Pegatron Technology Corp., are making the new phones, the Journal said.

Verizon Communications Inc., which co-owns Verizon Wireless with Vodafone Group Plc, rose 8 cents to $30.45 in New York Stock Exchange composite trading.

AT&T climbed 27 cents to $26.51. Apple advanced $1.49 to $232.39 on the Nasdaq Stock Market.