BERKELEY, Calif. — The number of international students attending American colleges and universities has nearly rebounded from a slump that followed the 2001 terrorist attacks, which triggered tough new visa restrictions and closer monitoring of foreign scholars.

During the 2006-07 academic year, nearly 583,000 international students took classes at U.S. schools, just 3,000 fewer than the record enrollment set just before the crackdown began, according to a recent report from the State Department and the nonprofit Institute of International Education.

Vance Gram, 26, a graduate student from Norway who is studying political science at the University of California, Berkeley, said the nation is more welcoming to international students than a few years ago.

"There's been something of a release from the grip of fear and distrust of anything foreign," said Gram, who has been in and out of the United States for years. "And America is more relaxed now than even two, three years ago, never mind five."

The enrollment figures were welcomed by government and academic officials who have worked to attract foreigners.

"This is a hugely important economic investment as well as an investment in human capital," said Tom Farrell, deputy assistant secretary for academic programs at the State Department, which released the report last month.

"We believe that people who study and learn here with us are better able to work with us later in their careers."

For years, U.S. schools made it easy for students from other countries to study here for long periods. But after one of the Sept. 11 hijackers entered the country on a student visa, the Bush administration got strict, adopting visa restrictions and reforms that allowed the government fast access to foreign students' information. The FBI also worked closely to keep tabs on international students and watch for evidence of terrorism.

After enrollments declined, some officials grew concerned about the dwindling numbers because international scholars help keep the United States competitive in the global market and contribute $14.5 billion a year to the economy. Karen Hughes, undersecretary for public affairs at the State Department, described the students as "the single most important public diplomacy tool of the last 50 years."

In January 2006, Secretary of State Condoleezza Rice and Secretary of Education Margaret Spellings co-hosted a summit attended by college presidents. The goal: to recruit more foreign students to U.S. schools.

That resulted in new grants to help foreign students study in the U.S., stepped-up recruiting in places such as India and China, and the hiring of new consular officials to expedite student visa applications.

Even now, Gram said, applying to study in the U.S. is not without hassles.

"There are so many tedious and seemingly unneeded requirements in visa regulations and so forth," he said. "I think that still puts people off, so they end up going other places."

Pui-Wa Li, an environmental engineering student from Hong Kong who is now studying at UC Berkeley, considered studying in Europe or Asia. But she was ultimately drawn to the United States by its "open, friendly climate" toward foreign scholars.

But some immigration-control advocates question the benefits of having non-Americans taking up desks and dorm rooms at U.S. institutions, which are seen as a back door into the country.

"It's being used in a way it was not originally intended to be used," said Steve Camarota, research director for the Center for Immigration Studies. "It farms out U.S. immigration policy to schools, who may or may not have the best interests of U.S. policy in mind."

Foreign student enrollment peaked at 586,000 in 2002-03, the year the visa restrictions took effect. It dropped steadily each of the next three years, before increasing 3.2 percent this year.

According to the report, India sends more scholars to U.S. institutions than any other foreign country — nearly 84,000 in 2006, a 9.6 percent increase over the prior year. China is second, followed by South Korea.

The biggest percentage growth was among students from Saudi Arabia. Nearly 8,000 students from that country attended American colleges and universities in 2006-07, a 128 percent increase over 2005-06.

The University of Southern California enrolls the greatest numbers of international students — more than 7,000, followed by Columbia University and New York University.

For some students, the decision to come to the United States was simple: The U.S. educational system remains among the best in the world. Others said the dip in the number of foreign students in the U.S. looked like their chance to break into a competitive field.

If fewer students come to the U.S., "there's less competition, more advantages," said Li, 19. "It's like buying stocks — when you buy low, you earn more."