US President Donald Trump's administration has ordered US embassies around the world to stop scheduling appointments for student visas as it prepares to expand social media vetting of such applicants.

An official memo said social media vetting would be stepped up for student and foreign exchange visas, which would have "significant implications" for embassies and consulates.

It comes during a wide-ranging Trump crackdown on some of America's most elite universities. He sees these institutions as too left-wing – accusing them of failing to combat antisemitism when pro-Palestinian protests have unfolded on campuses.

Responding to the move, China called on the US to protect international students.

"We urge the US side to earnestly safeguard the legitimate rights and interests of international students, including those from China," an official was quoted as saying. Hundreds of thousands of Chinese students attend US universities.

The universities themselves are likely to be disquieted as well. Many of them rely on foreign students for a significant chunk of their funding – as those scholars often pay higher tuition fees.

Foreign students who want to study in the US are usually required to schedule interviews at a US embassy in their home country before approval.

State department spokesperson Tammy Bruce told reporters on Tuesday: "We take very seriously the process of vetting who it is that comes into the country, and we're going to continue to do that."

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The memo, viewed by the BBC's US partner CBS News, directed US embassies to remove any unfilled appointments from their calendars for students seeking visas, but said those with appointments already scheduled could go ahead.

The pause would last "until further guidance is issued", Secretary of State Marco Rubio wrote.

The memo also said the state department was preparing for an "expansion of required social media screening and vetting" applicable to all student visa applications.

• Trump administration to 'aggressively' revoke visas of Chinese students

It did not spell out what the vetting would look for.

The Trump administration had already enhanced its vetting of student social media, according to a report by the Guardian in March, which linked the move to a broader crackdown on pro-Palestinian demonstrations on campuses.

In April, the US Department of Homeland Security (DHS) stated that it would consider "antisemitic activity on social media and the physical harassment of Jewish individuals as grounds for denying immigration benefit requests".

As part of the broader crackdown, Trump's team has frozen hundreds of millions of dollars in funding for universities and moved to deport students, while revoking thousands of visas for others. Many of these actions have been blocked by the courts.

The White House has accused some US universities of allowing pro-Palestinian activism on campus to be hijacked by antisemitism.

Universities have accused the Trump administration of trying to infringe on free speech. Critics say the new policy on social media vetting represents a further violation of the rights that are supposed to be enshrined by the First Amendment in the US Constitution.

Trump has throughout his presidency countered that he is working to defend free speech.

Harvard University has been the focal point of the president's ire; he has frozen $2.65bn (£1.96bn) in federal grants to the institution and has sought to put other federal funding worth $100m under review.

The university's president has said the cuts will "hurt" the country, not just Harvard, because academics were conducting research deemed "high-priority" by the government.

Last week, Trump also revoked Harvard's ability to enrol international students or host foreign researchers. A federal judge blocked the policy.

If the measure is ultimately allowed, it could deliver a devastating blow to the university, where more than a quarter of students are from overseas. Students protested against the move at the university's campus near Boston on Tuesday.