Verizon Wireless and Nextel Communications said they resolved disputes over airwaves and trademark names, ending a 15-month legal battle between the two American mobile phone providers.

Verizon Wireless, the second-largest American wireless carrier, said it won’t challenge a government decision to allow Nextel to swap airwaves worth as much as $4.86 billion. In return, Reston, Va.-based Nextel will allow Verizon Wireless to use the push-to-talk name that it has used to promote Nextel service.

The agreement with Verizon Wireless removes one of the biggest obstacles Nextel faced in getting new airwaves to expand its service, Lehman Brothers analyst Blake Bath wrote in a note yesterday. Investors had been concerned that an agreement with American regulators to swap airwaves that interfere with emergency frequencies may be tied up in the courts.

“It’s a very big positive for Nextel,” said an analyst at ABN Amro Asset Management in Chicago, Charles Ullerich. “Nextel has been constrained in some of its markets regarding spectrum.” Mr. Ullerich helps manage $1.2 billion in high-yield debt, including Nextel securities.

Shares of Nextel, the no. 1 seller of walkie-talkie mobile-phone service, rose $1.06, or 4%, to $27.15 at 12:21 p.m. New York time in Nasdaq Stock Market composite trading. Verizon Communications Inc., which owns Verizon Wireless with UK-based Vodafone Group Plc, rose 53 cents to $40.51 in New York Stock Exchange composite trading.

“It’s time to move on,” said a spokesman for Bedminster, N.J.-based Verizon Wireless, Jim Gerace, in an interview.

Verizon Wireless, which had said Nextel was getting replacement airwaves too cheaply and that they should be auctioned, dropped its opposition to clear the way for the companies to work together on regulatory issues, Mr. Gerace said. Verizon and Nextel face increasing competition from Cingular Wireless LLC, which last week completed its $41 billion purchase of AT &T Wireless Services to become the largest American carrier.

In July, the Federal Communications Commission agreed to let Nextel hand back airwaves valued at $1.6 billion and pay $3.25 billion for new airwaves the government says are worth $4.86 billion. Nextel was ordered to pay the difference by funding the costs of moving signals by police and fire agencies to different channels and pay any remaining gap to the government. Last month, Nextel said the FCC was overcharging it by $452 million.

“We always like competitors to get along,” an analyst at Marquis Investment Research in Chicago, Greg Gorbatenko, wrote in a note yesterday. “It keeps more money in the telecom pie and less out of the lawyer pie.”

Verizon Wireless spent $1.3 million in the first half of the year, partly in an attempt to derail Nextel’s plan to win airwaves from the FCC. Nextel spent $1.92 million in lobbying efforts.

Emergency-services radios don’t work in parts of some cities such as New York, Honolulu, and Portland, Ore., because Nextel shares spectrum in the 800-megahertz band with police and firefighters, creating interference. The FCC doles out the airwaves needed to transmit wireless calls and information.

The channels Nextel, the no. 5 American mobile-phone operator, will get for returning those used by police and fire officials will help the company expand wireless Internet services.

Pending lawsuits over trademarks on the push-to-talk name will be dismissed, the companies said in a statement. Nextel, which uses push-to-talk to promote its service, agreed to forego any trademark or ownership rights to the push-to-talk phrase.

Verizon Wireless introduced push-to-talk service in August 2003 after filing a lawsuit the previous month disputing Nextel’s right to the phrase. In April that year, Nextel had been approved to get a trademark for the phrase. Verizon Wireless sells one push-to-talk phone and plans to introduce more, Gerace said. He wouldn’t say when.

“The agreement paves the way for a timely conclusion to the FCC’s spectrum solution and we feel should bring the process to a close by year-end,” A.G. Edwards Inc. analyst Gregory Teets wrote in a note to investors. He has a “buy” rating on Nextel shares. A.G. Edwards owns Nextel debt.