Verizon Communications Inc. told federal regulators it would keep supporting low-cost wireless service for three years if it is allowed to buy TracFone, a sign of deepening negotiations in the carrier’s effort to control a giant in prepaid cellphone plans.

“We’re very comfortable to make that commitment to…continued participation in Lifeline for the next three years in any geography where TracFone provides Lifeline services today,” Ronan Dunne, Verizon’s chief of consumer services, said in an interview Thursday. The carrier will also provide ultrafast fifth-generation, or 5G, service to Lifeline customers within six months of the deal’s closing, he added.

Lifeline is a federal subsidy for low-income phone users, such as those receiving Medicaid or public-housing funds. The Communications Workers of America union and other public-interest groups have criticized the proposed merger partners for not detailing specific plans to keep supporting the program.

Verizon last year agreed to buy TracFone for up to $6.9 billion, a price that includes $650 million contingent on certain performance targets. TracFone, a unit of Mexican telecom operator America Movil SA B, served nearly 21 million U.S. customers at the end of March through brands like StraightTalk, Net10 and Simple Mobile. About 1.7 million subscribers use Lifeline through its SafeLink Wireless service.

Mr. Dunne and TracFone Chief Executive Eduardo Diaz Corona discussed their proposed commitments last week in a virtual meeting with acting Federal Communications Commission Chairwoman Jessica Rosenworcel, according to a recent filing. Companies sometimes pledge to agree to certain regulatory conditions in an effort to speed a deal’s approval. A spokeswoman for Ms. Rosenworcel declined to comment on the pending deal.

Public Knowledge, a Washington-based public-interest group, has urged the commission to protect cash-strapped TracFone users from efforts to upsell or discontinue their service.

The FCC “can ensure that Verizon remains true to its word by adopting the enforceable merger conditions,” including a five-year commitment to Lifeline participation and a freeze on some rates, the group wrote in a May filing.

The recent discussions show the companies and their opponents sharpening their arguments with a focus on Lifeline. The program and a separate Emergency Broadband Benefit launched during the coronavirus pandemic have helped millions of Americans stay linked to work, school and healthcare during the crisis.

Verizon also discussed its plans to keep supporting such programs in the FCC meeting, though Mr. Dunne said the more disruptive topic of divestitures “hasn’t come up in any conversation.” TracFone is a group of brands that market service provided over other networks, including Verizon’s. Verizon plans to shift many of the TracFone users relying on AT&T Inc. and T-Mobile US Inc. systems over to its own network if the deal is approved.

“The opportunity is to bring real facilities-based competition into the prepaid segment,” he said. “It would be counterintuitive to look at disposals in that context.”

Mr. Dunne said Thursday that the company still expects to close the deal this year.

Write to Drew FitzGerald at andrew.fitzgerald@wsj.com