The number of foreign students enrolled in American universities declined slightly in the 2004-5 academic year, according to a survey to be released today, suggesting that a more significant drop that took place in the aftermath of the terrorist attacks in 2001 might be abating.

About 565,000 students from foreign countries were studying in undergraduate and graduate programs at American universities, a decline of 1 percent from the previous academic year, according to an annual survey by the Institute of International Education that was financed by the State Department.

A survey released by the organization last year showed that foreign student enrollment had declined by 2.4 percent in the 2003-4 academic year, the first decrease in foreign students in three decades.

A related survey released last week by the Council of Graduate Schools showed that the number of international students entering American graduate schools increased 1 percent this year. The report was based on a survey of a sample of graduate institutions.

University officials have offered several reasons for the drop in foreign students after 2001, including difficulties students have experienced in obtaining visas, especially in scientific and technical fields, and the increased cost of tuition. There has also been more competition from universities in Britain, Australia and New Zealand, as well as a significant expansion in the capacity of universities in India and China.

India, with more than 80,000 students, and China, with more than 62,000, send the largest number of students to American universities, the Institute of International Education survey found. Many students from South Korea, Japan, Canada and Taiwan are also enrolled here.

A growing number of American students are studying abroad, the institute also reported. The number increased 9.6 percent in the 2003-4 academic year, the institute found, after growing by 8.5 percent the previous year. More than 191,000 Americans are studying for academic credit in international universities, with notable increases in China and India.

Foreign students in the United States spend about $13.3 billion in tuition, living expenses and related costs. In many schools they account for the majority of graduate students in science and engineering.