* European economy "teetering"
* World's overall economic recovery won't be slowed
* Healthcare costs, jobs to weigh on U.S. economy (Adds comments on China, financial reform bill, updates speech as delivered)
By Scott Malone
BOSTON, May 24 (Reuters) - The U.S. economy faces major problems while Europe's is "teetering," the head of General Electric Co (GE.N) told a class of graduating college students on Monday.
"We are at an unprecedented moment in the history of our country. There is economic and social anxiety," said Jeff Immelt, chairman and chief executive of the largest U.S. conglomerate. "Europe appears to be teetering."
Still, the risk that the Greek debt crisis could drag down other European economies does not appear to be enough to derail the world's overall economic recovery, he told reporters after addressing Boston College's commencement.
"It's going to be slow growth in the economic region, but look, I'm 28 years with GE and I can't remember when Europe was fast growth," Immelt said. "I think the U.S. economy is very good right now and improving. We have to see what happens in Europe, but I don't think it's enough to slow the recovery, I really don't."
China's economy -- a key growth market for GE, the world's largest maker of jet engines and electricity-producing turbines -- "remains reasonably robust," Immelt said.
The U.S economy will have to confront problems ranging from the rising cost of healthcare to the loss of many of the manufacturing jobs that once sustained the nation's middle class, Immelt said at Boston College, where GE does extensive recruiting. The company currently employs some 270 alumni of the school.
"Look, it's a mess out there. There are some real problems that need to be fixed. I could really bum you out if I wanted to," Immelt told the graduates. "Your country will be better coming out of the financial crisis if we learn a few lessons: that real, honest, ethical leadership matters, that the U.S. cannot prosper today as just a service economy."
Improving the U.S. healthcare system is a pet cause of Fairfield, Connecticut-based GE, which is a major maker of medical imaging devices. GE aims to invest some $6 billion over the next four years in ventures it hopes will help lower the cost of healthcare.
"The problems with the American healthcare system are real and will require great determination," Immelt said.
The GE chief, who was awarded an honorary doctorate in business administration, also said the world needs to come to terms with the growing gap between rich and poor, both in the United States and abroad.
"The global economy will not tolerate a few people getting rich while other people get poor," said Immelt, who earned his Masters of Business Administration at nearby Harvard Business School.
He also told reporters he was confident that GE, which runs a hefty finance operation, was prepared to cope with any changes to U.S. regulations resulting from the sweeping financial reforms passed last week by the U.S. Senate.
"Is it perfect? No, but could we live with what's passed the Senate? Sure," Immelt said. "We'll have to adjust to new standards and we're ready for that."
Last year, some observers suggested the reforms could force GE to spin off its GE Capital unit, an idea the company fought. (Reporting by Scott Malone, editing by Dave Zimmerman and John Wallace)