NEW YORK — Verizon Wireless on Monday said it has agreed to sell some wireless spectrum rights to T-Mobile USA and to swap others, in a continuing quest to get regulators to approve a bigger spectrum deal it has worked out with a consortium of cable companies and another wireless carrier.

The deal would improve the ability of both companies to offer fast wireless data services.

T-Mobile, the fourth-largest US wireless company, is starved for spectrum, compared to larger competitors, and regulators are apt to favor a deal that would improve its position.

Neither T-Mobile nor Verizon said what T-Mobile would pay Verizon. Sanford Bernstein analysts estimated the amount at $260 million, figuring that T-Mobile is getting the spectrum at a roughly 50 percent discount.

The deal is contingent upon Verizon’s getting government approval for three deals to buy spectrum from cable companies and Leap Wireless for a total of about $4 billion. Those deals, struck in November and December, have met resistance from public-interest groups who say the cellphone company, already the nation’s largest, does not need more spectrum and should not be cozying up to competitors.

T-Mobile had also opposed the Verizon-cable deals, saying they would place an ‘‘excessive concentration’’ of spectrum in Verizon’s hands. Verizon is the largest cellphone company and has a strong spectrum position already.

Harold Feld, at public-interest group Public Knowledge, said Verizon is trying to ‘‘buy off’’ T-Mobile.

To get deals with cable companies and Leap cleared, Verizon has offered to auction other airwaves it isn’t using.