BERLIN/WASHINGTON (Reuters) - Volkswagen is struggling to agree with U.S. authorities a fix for vehicles capable of cheating emissions tests, a VW source said on Tuesday, showing how relations between the two sides remain strained four months after the cheating came to light.

A Volkswagen company logo sits atop the VW factory in Wolfsburg, Germany November 20, 2015. REUTERS/Ina Fassbender

The source said the German carmaker would hold further talks with the Californian Air Resources Board this week and with the U.S. Environmental Protection Authority (EPA) next week, and still hoped to reach a solution by a mid-January deadline.

But finding a fix was proving more difficult than expected, in part because this involved producing new components which then required testing, said the person, who declined to be named as the talks are confidential.

The difficulties highlight the lack of progress VW has made in winning back the confidence of U.S. regulators and drivers almost four months after it admitted to cheating diesel emissions tests and promised to turn over a new leaf.

The U.S. Justice Department is suing Europe’s biggest carmaker for up to $48 billion for allegedly violating environmental law - a reminder of the carmaker’s problems nearly four months after its emissions scandal broke.

The move threw VW’s U.S. problems back into focus after it seemed to be recovering ground in Europe, sending its shares down more than 8 percent to a six-week low on Tuesday.

“The announcement serves as a reminder/reality check of VW’s still unresolved emissions issues,” Goldman Sachs analysts said of the lawsuit.

VW Chief Executive Matthias Mueller is expected to meet EPA representatives and politicians in Washington next week after visiting the Detroit Auto Show, the VW source said, on what will be Mueller’s first trip to the United States since the scandal broke in September.

VW declined to comment on the progress of talks with the EPA, on whose behalf the U.S. Justice Department filed the lawsuit, or on Mueller’s plans.

According to a Reuters review of the U.S. complaint, VW could in theory face fines of as much as $37,500 per vehicle for each of two violations of the law; up to $3,750 per “defeat device”; and another $37,500 for each day of violation.

The complaint says illegal devices to impair emission control systems were installed in nearly 600,000 vehicles in the United States. (here)

U.S. lawsuits are typically settled at a fraction of the theoretical maximum. Goldman has estimated the likely costs at 500 million euros ($534 million).

A senior U.S. Justice Department official said the judge was not expected to rule that every car should be charged for all four counts, but said the department had set the bar high, knowing it would come down.

Another senior departmental official said a settlement would likely be “in the billions”, without elaborating. Both officials declined to be named.

PUBLIC HEALTH

VW shares pared losses to trade down 4.4 percent at 120.9 euros by 1530 GMT, still 21 percent lower than before the company’s cheating came to light on Sept. 18.

The shares had been recovering after VW announced last month it had agreed simple fixes for 8.5 million affected vehicles in Europe, and sharply lowered the number of cars affected by a separate understatement of carbon dioxide emissions.

The Justice Department said in its complaint it was seeking “appropriate steps” from the German group to make nearly 600,000 vehicles compliant with U.S. emissions rules.

“Car manufacturers that fail to properly certify their cars and that defeat emission control systems breach the public trust, endanger public health and disadvantage competitors,” said Assistant Attorney General John C. Cruden for the Justice Department’s Environment and Natural Resources Division.

Evercore ISI analyst Arndt Ellinghorst, who recommends buying VW shares, said VW should do its utmost to allay concerns in the United States.

“We would argue that VW should go for the broadest and even most expensive buy back option in order to restore customer and dealer relationships in the U.S.,” he wrote.

“The more VW spends on fixing its U.S. problems, the lower its legal charges will be at the end.”

German politicians expressed concern on Tuesday that a hefty U.S. fine could hit jobs. VW employs around 270,000 people in Germany.

($1 = 0.9298 euros)

(This story corrects the maximum penalty from $90 billion to $48 billion in the fifth paragraph and the terms of the penalties in the tenth paragraph)