Trump's administration this week said it would specifically target permissions for Chinese students, in its latest broadside against US higher education.

But when asked Friday what message he would send to Chinese college students in the country, Trump insisted: "They're going to be ok. It's going to work out fine."

"We just want to check out the individual students we have. And that's true with all colleges," he told reporters.

The softer tone comes after a judge on Thursday extended a temporary block on Trump's bid to prevent Harvard from enrolling international students.

US Secretary of State Marco Rubio vowed on Wednesday to "aggressively" revoke visas to students from China. Rubio has already yanked thousands of visas, largely over students' involvement in activism critical of Israel's offensive in Gaza, but also over minor traffic violations and other infractions.

The Trump administration has been in an ongoing showdown with academia, and Harvard in particular, demanding it provide a list of students that the government is interested in, something the prestigious university has declined to do.

"I don't know why Harvard's not giving us the list. There's something going on because Harvard is not giving us a list," Trump said Friday.

"They ought to give us a list and get themselves out of trouble," he insisted, suggesting that "they don't want to give the list because they have names on there that supposedly are quite bad."

At graduation ceremonies this week, Harvard University president Alan Garber received a one-minute standing ovation when he called for universities to stand "firm" in the war the Trump administration has waged against students and schools.

"We want people that can love our country and take care of our country and cherish our country," Trump said Friday.

International students on average make up just under six percent of the US university population -- far below Britain, the second top destination for international students, where the figure is 25 percent.