Major American universities -- including Harvard, Princeton and Columbia -- have been forced to cancel classes because of the coronavirus and move lessons online, affecting tens of thousands of students.

The US government has refrained from imposing an official ban so the often privately run institutions are each grappling with how best to deal with the fast-moving outbreak. Ahead of the start of spring break at the end of this week, Harvard on Tuesday announced it would transition to having all classes online by Monday 23 March.

The university, located in Cambridge, Massachusets, asked its 36,000 graduate and undergraduate students not to return to campus after the spring recess and to continue studying remotely "until further notice."

"The goal of these changes is to minimize the need to gather in large groups," Harvard president Lawrence Bacow said in a statement posted on the university's website.

Without going quite so far, the Massachusetts Institute of Technology (MIT), also based in Cambridge, canceled all gatherings likely to attract at least 150 people until May 15. Classes with 150 or more students will move online, starting this week, it added.

In New York, Columbia, New York University and Fordham have all announced that they are switching to remote learning. Princeton University in New Jersey said it would move all lectures and seminars online from March 23 to at least April 5, as it cancelled events of more than 100 people.

On the other side of the country, in California, at least five universities, including Berkeley and Stanford, have suspended all or most of their in-person classes. A spokesperson for the American Council of Education (ACE) said it was "impossible to say" how many schools and students had been affected because "the situation changes all the time."

ACE president Ted Mitchell told the Los Angeles Times the coronavirus was "probably the greatest short-term challenge facing higher education in a generation."