Negotiators are nearing a settlement on a second batch of nearly 80,000 vehicles caught up in Volkswagen’s diesel emissions scandal, a federal judge said Thursday.

U.S. District Court Judge Charles Breyer in San Francisco said he was “very pleased” to reveal that negotiators had made “substantial progress” toward a deal over vehicles with 3-liter V-6 diesel engines fitted with software to evade emissions standards.

He did not offer any details on what the deal could include, though a separate settlement involving 2-liter four-cylinder vehicles fitted with similar software involves vehicle buybacks, thousands of dollars in compensation per owner and environmental remediation efforts.

Settlement mediator Robert Mueller, former director of the FBI, is leading the latest round of talks and informed Breyer privately of the progress.

“There have been continual meetings,” Breyer said. “I am very optimistic that we will achieve a resolution.”

The revelation comes about a week after Breyer approved the nearly $15 billion settlement between Volkswagen, consumers, the Department of Justice, Environmental Protection Agency, Federal Trade Commission and California regulators over 2-liter diesel carsThat deal covered more than 470,000 vehicles.

Breyer said he plans to sign a gag order to prevent parties from discussing details of the potential deal.

The 2-liter deal gives consumers a choice between a buyback or a payout and a free fix if VW can get the repairs approved by the EPA. Last week, VW’s North American CEO Hinrich Woebcken told reporters at the debut of the new Atlas SUV in Santa Monica, Calif., that a solution to repairing the cars will be found.

“We have very good engineers working on the solution,” he says. He also says he doesn’t believe loyalty to the VW brand has been shaken by the debacle, saying that when he talks to diesel-car customers, “10 out of 10 love their cars” and that they are willing to give the embattled brand a second chance.

Buybacks range in value from $12,475 to $44,176, including restitution payments, and vary based on mileage. People who opt for a fix will receive payments ranging from $5,100 to $9,852, depending on the book value of their cars.

VW attorney Sharon Nelles said Thursday that more than 370,000 VW owners have already registered for the settlement. About 25% have submitted papers to make a selection.

She said that VW’s call center is fielding 6,500 calls per day from consumers, up from 1,700 before Breyer approved the deal.

Some customers have reported long wait times. Breyer noted the complaints and asked for patience as VW increases staffing. He also sympathized with the vehicle owners.

“This is, for many, many people, not only their major asset but also their principal necessity,” he said. “So I understand the emotional strain and frustration in having something so important to their day-to-day life that they can’t quickly address and resolve.”

Contributing: Chris Woodyard

Follow USA TODAY reporter Nathan Bomey on Twitter @NathanBomey.