SAN FRANCISCO/WASHINGTON -- Volkswagen AG and lawyers for owners and the U.S. government have made "substantial progress" toward reaching a final agreement by late June, a federal judge said today.

But major issues remain, including how much the world's No. 2 automaker may have to pay in fines, which could run in the billions of dollars, to federal and state regulators for violating U.S. clean air rules, as well as an ongoing U.S. Justice Department criminal probe.

U.S. District Judge Charles Breyer in San Francisco reiterated that a settlement will include substantial monetary compensation for U.S. owners of 482,000 polluting vehicles that emit up to 40 times legally allowable pollution.

The scandal has hurt VW's global business as well as its reputation and led to the departure of its CEO and other executives. The scandal erupted last September after the company admitted using sophisticated secret software in its cars to cheat exhaust emissions tests. As many as 11 million vehicles worldwide have been affected.

At a brief court hearing, Breyer said lawyers for car owners suing Volkswagen and the U.S. Justice Department, Environmental Protection Agency (EPA), Federal Trade Commission, the state of California and the company were on track to file the final proposed settlements by June 21.

The "parties ... have reported that in the month since we last met they have made substantial progress in intensive daily efforts to finalize the agreement, and most importantly are on track to meet the court's deadline," Breyer said.

The U.S. settlement would also include an environmental remediation fund to address excess emissions and a fund to promote green automotive technology.

Elizabeth Cabraser, lead lawyer for the U.S. car owners, and a Volkswagen spokeswoman both said the parties were pleased with the continued progress and planned to finalize the agreements next month.

Breyer said engineering studies and testing were continuing toward a resolution for the owners of 80,000 larger 3.0-liter vehicles but offered no timetable.

The vehicles emitted up to nine times the legally allowable pollution, and it was not clear if the automaker will offer to buy back the larger 3.0-liter Porsche, Audi and VW SUVs and cars under investigation.

The EPA ordered VW last September to stop selling all new 2016 2.0-diesel vehicles. The ban was extended to 3.0-liter VW, Porsche and Audi diesel vehicles in November. The order remains in effect.

After the June 21 deadline the agreement faces a public comment period and must get final judicial approval, which could come at a July 26 hearing.

Provisions adequate

Meanwhile, Volkswagen believes it will not need to raise provisions of 16.2 billion euros ($18.1 billion) it has already made for its diesel-emissions cheating, a source familiar with the matter said today.

"We know the sum we are facing as of today," the source said before a federal judge reported "significant progress" was being made towards a final agreement between VW and the U.S. by late June.

In April, Volkswagen agreed to a framework settlement with authorities in the United States to buy back or potentially fix about half a million cars, after admitting it masked the level of pollution from its cars using cheating software, plunging the carmaker to a 4.1 billion euros operating loss for 2015.

The company could still face further costs, including from a federal investigation that could lead to criminal charges, and potential class-action suits.