In another sign that the recession in Europe has hit consumer spending, car sales there fell in May and reached their lowest level in that month since 1993.

The data likely will press U.S. car companies, particularly General Motors Co. (NYSE: GM) and Ford Motor Co. (NYSE: F), to further question whether they want to keep a presence in Europe, at least at current levels. The trend also may force them to find joint venture partners to share manufacturing costs, although unions and national governments may resists this as a means to save jobs.

The figures should also raise concern about the strength of Europe’s largest nation by GDP — Germany.

The European Auto Manufacturers’ Association reported on new passenger car registrations:

In May, demand for new passenger cars declined by 5.9% in the EU, reaching 1,042,742 units. In absolute figures, this is the lowest level recorded for a month of May since 1993 when new registrations stood below one million. Five months into the year, a total of 5,070,840 new cars were registered in the region, or 6.8% less than in the first five months of 2012.

In May, most major markets faced a downturn ranging from -2.6% in Spain to -8.0% in Italy, -9.9% in Germany and -10.4% in France. The UK was the only country to post growth (+11.0%). Overall, the EU registered 1,042,742 new cars, or 5.9% less than in the same period last year.

From January to May, Spain and Germany saw their market shrink by 5.8% and 8.8% respectively, while Italy (-11.3%) and France (-11.9%) recorded a double-digit decline. The UK continued its positive trend, expanding by 9.3%. In total, the 5,070,840 new cars registered over five months represented a 6.8% decrease in demand compared to the same period last year.

The figures for GM were brutal. Sales dropped 11.3% to 87,943 , and its market share fell from 9% to 8.4%. In Ford’s case, the numbers were a bit better. Sales fell only 0.3% to 82,953, and its market share rose from 7.5% to 8%. The unimaginable now seems possible — Ford could outsell GM in Europe within a few months, if the trend continues. Incidentally, Chrysler’s largest shareholder, Fiat, had a particularly poor month, with sales falling 10.8% to 72.227. Its market share dropped from 7.3% to 6.9%. The irony of the recent Fiat deal under which it controls Chrysler is that the U.S. company has done far better than its parent. This could press Fiat to buyout all of Chrysler, which has been rumored, and set an IPO to cover the acquisition costs.

Perhaps the worst news for the U.S. car companies is that behemoth Volkswagen, that largest car company in sales in the region, posted fairly good numbers. Sales dropped only 0.2%, much less that the regionwide number, to 264,768. Market share moved higher, from 24.6% in May of last year to 25.4% this year. VW currently has a much larger share in Europe than GM has in its home market in the United States, where it is the top car manufacturer by sales.

GM has lost money in Europe since 1999, for a total of $13 billion, and changes in management have not helped right the situation. The U.S. car company has made some attempts to cut these losses, but the efforts have been plodding, as powerful local unions have thwarted the moves.

GM continues to do well in the United States, as well as China, where it is the top car company in the world’s largest market. GM management is understandably reluctant to abandon a market as large as Europe, but for the sake of its investors, it should ignore the path of staying. Not only is the market in Europe contracting, and could for years, but buyers in the region do not want GM cars, which the numbers shout very loudly.

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