Regulators in California on Tuesday formally rejected Volkswagen’s plan to fix its polluting diesel engines, underscoring their frustration with the German automaker’s ability to repair its defective vehicles.

The California Air Resources Board, which is investigating VW’s use of a so-called defeat device to cheat on diesel emissions tests, said that a recall plan presented in November and December was “incomplete, substantially deficient and falls far short of meeting the legal requirements” to be approved. The state agency added that VW was taking too long to devise a fix.

The Environmental Protection Agency, which is working with California regulators on the VW fraud, had already said it was not satisfied with the recall plan and requested more information from the company.

Investigators have grown increasingly annoyed with VW since the carmaker admitted in September to the use of fraudulent devices that lowered emissions during testing. Last week, the Justice Department, which had opened its own investigation, filed a civil complaint against the company, accusing it of exceeding E.P.A. air quality standards and violating the Clean Air Act.

It is in that context that Matthias Müller, VW’s chief executive, had requested to meet on Wednesday with the E.P.A. administrator, Gina McCarthy, to discuss the emissions problem, which affects 600,000 vehicles in the United States and up to 11 million vehicles worldwide.

Jeannine Ginivan, a spokeswoman for VW, acknowledged the shortfalls of the December submission and suggested that the company has had “constructive conversations” with the California air board.

But California regulators said VW had failed so far to properly describe its use of the defeat devices and how those would be affected by the proposed recall plan. The carmaker, the air board said, also did not provide enough details about its technical fixes to allow regulators “to evaluate whether they could be successful or are even technically feasible.” In addition, it said VW had not explained how its recall plans would affect the engine’s operation and performance.

The E.P.A. said in a statement that it agreed with California “that Volkswagen has not submitted an approvable recall plan to bring the vehicles into compliance and reduce pollution. E.P.A. has conveyed this to the company previously.”

Separately, a federal judge in San Francisco picked Robert Mueller, the former chief of the Federal Bureau of Investigation, to help steer VW toward a settlement with car owners. Mr. Mueller has agreed to mediate negotiations as “special master” in the case consolidating more than 500 consumer lawsuits. In December, the automaker hired Kenneth Feinberg, a prominent compensation fund specialist, to devise and administer an out-of-court program for consumer claims.