As the European crisis intensifies, a growing number of companies in the United States are warning investors that sales in the region are slowing and could get much worse.


In the technology industry, one of the most exposed to Europe and an engine of the American recovery, Cisco, Dell and NetApp have all recently pointed to unexpected weakness in European sales. Other areas with major exposure to the Continent, including automakers and industrial companies, are beginning to voice similar cautions.


Just a few months ago, market watchers were optimistic that the American economy had decoupled from Europe’s problems, able to grow even as the Continent faltered.


While most of the focus has been on oppressive debt and debilitated banks in the euro zone, concerns are shifting to the drag that recession in Europe is exerting on the global economy. Over the weekend, President Obama reflected the growing anxiety by saying that Europe’s economy is “starting to cast a shadow on our own as well” and that it was partly to blame for the recent slowdown in job creation in the United States.


The economy of the European Union, which holds the 17 nations that use the euro currency and 10 others, is a larger economic unit than the United States or China.


Corporate profits have been one of the brightest spots in the American economy, but the decline in European revenues is part of the reason that analysts have recently ratcheted down their expectations for profit growth in the second quarter. In the case of technology companies, analysts say they believe that about a third of all revenue comes from Europe.


Through the first few months of this year, when technology stocks were leading markets up, the networking giant Cisco was sharing in the good times, ready to leave behind recent difficulties tied to bad acquisitions.


Last month, though, Cisco’s chief executive acknowledged that the company’s economic outlook in Europe had “gotten worse,” helping to push the company’s shares down 11 percent in one day.


A. M. Sacconaghi, a technology analyst at Sanford C. Bernstein & Company, said, “As push has come to shove, we have started to see a real shift in outlook.”


Prospects for the European economy darkened in recent days as surveys showed that manufacturing across the euro zone contracted in May and the unemployment rate climbed to a record 11 percent. On Monday, Portugal’s finance minister said that the country’s growth rate next year would be lower than expected.


Manufacturing has also slowed in India and China, according to data released last week, threatening two of the most reliable drivers of global growth. In the United States, job creation slowed to the weakest level in a year.


The gloomy news sent financial markets around the world tumbling through last week, with the Dow Jones industrial average falling into the red for the year. Share prices were mixed around the globe on Monday; stocks in the United States were flat and Europe’s were up slightly.


A weaker Europe has meant a stronger dollar, making American products more expensive. In Asia, several countries rely heavily on exports to Europe and are consequently slowing down in manufacturing, which in turn lowers Asian demand for imports. Even companies around the world that are not dependent on exports are vulnerable as consumer confidence is eroded.


The biggest fear was that Greece’s potential departure from the euro currency would set off a financial crisis like the one in 2008. American banks have tried to reduce their holdings of bonds issued by countries in Europe’s troubled southern periphery. But if payments and loans were frozen at European financial institutions, it would quickly spread to American banks and from there to the broader American economy.


“I don’t think anyone is fully prepared for a disorderly exit of Greece from the single currency,” said Edward Marrinan, the head of macro credit strategy at RBS.