Verizon Communications Inc., parent of the country’s largest cellphone carrier, on Thursday said its net income rose 13 percent in the second quarter as its wireless arm pulled in record profits.

Verizon has one foot in the wireless world and one in the traditional, wired-phone world. In the latter, results were notably weaker. Like other phone companies, Verizon is losing landlines, but has been compensating to some extent by signing up broadband customers. In the second quarter, that trend faltered, as it gained a net of just 2,000 broadband customers — the worst result in four years.

Chief Financial Officer Fran Shammo said the weak showing was in part due to Verizon ending the sale of DSL connections to people who don’t have landline phone accounts. The effort is part of an attempt to improve profitability. The wired-connection side of Verizon, which still employs nearly half of its workers, is running just above break-even.

Verizon has upgraded part of its phone network with optical fiber, a service it sells as FiOS. In locales where it hasn’t done that, it’s losing out to cable companies, who can offer much higher speeds than Verizon can with DSL.

The poor showing comes after Verizon Wireless struck a deal to market cable broadband from Comcast and Time Warner Cable in its stores, a move consumer advocates see as a capitulation by Verizon that will leave many areas with just one viable choice for home broadband: cable.

Overall, the New York-based phone company earned $1.83 billion, or 64 cents per share, in the April-to-June period, up from $1.61 billion, or 57 cents per share, a year ago. The latest earnings match the average forecast of analysts polled by FactSet.

Revenue rose 3.7 percent to $28.5 billion, also in line with analysts’ expectations.

Verizon stock fell nearly 3 percent Thursday, closing at $44.54, down $1.35. Shares had hit a 10-year high of $46.41 on Wednesday.