Former President Barack Obama is applauding Harvard University's decision to refuse the White House's demands that it change its policies or lose federal money, in his first social media post to criticise the Trump administration since at least Inauguration Day.

President Donald Trump is freezing more than $2bn (£1.5bn) in federal funds for Harvard because it would not make changes to its hiring, admissions and teaching practices that his administration said were key to fighting antisemitism on campus.

Obama, a Harvard alum, described the freeze as "unlawful and ham-handed".

He called on other institutions to follow Harvard's lead in not conceding to Trump's demands.

"Harvard has set an example for other higher-ed institutions – rejecting an unlawful and ham-handed attempt to stifle academic freedom, while taking concrete steps to make sure all students at Harvard can benefit from an environment of intellectual inquiry, rigorous debate and mutual respect," Obama wrote on social media.

The former president, who graduated from Harvard Law School in 1991, has rarely criticised or rebuked government officials or government policies on social media since leaving the White House almost a decade ago. His posts during the election typically extolled Trump's challenger, then-Vice-President Kamala Harris, and since Inauguration Day, he has mainly posted tributes, personal messages and thoughts on sports.

Obama is one of a handful of US political figures and university officials now speaking out against the Trump administration's attempts to reshape the country's top universities, through pressure to change what they teach and who they hire and threats to cut research funding.

Hundreds of faculty members at Yale University published a letter expressing their support for Harvard's decision to reject the Trump administration's demands.

"We stand together at a crossroads," the letter read. "American universities are facing extraordinary attacks that threaten the bedrock principles of a democratic society, including rights of free expression, association, and academic freedom. We write as one faculty, to ask you to stand with us now."

Many US universities receive some type of federal funding, which is mostly designated for scientific research in areas such as drug development.

Since Trump returned to office in January, elite institutions such as Stanford University have had to freeze hiring and cut budgets in the face of shrinking federal funds.

Some of the funding has been paused to press universities to take steps that the Trump administration says will fight antisemitism. Trump has accused them of failing to protect Jewish students during last year's campus protests against the war in Gaza and US support for Israel.

Stanford President Jonathan Levin and Provost Jenny Martinez on Tuesday said in a statement praising Harvard that "universities need to address legitimate criticisms with humility and openness".

"But the way to bring about constructive change is not by destroying the nation's capacity for scientific research, or through the government taking command of a private institution," they wrote.

While Columbia University ceded to some of Trump's demands earlier this month, Harvard became the first major US university to take the opposite approach.

"No government – regardless of which party is in power – should dictate what private universities can teach, whom they can admit and hire, and which areas of study and inquiry they can pursue," Harvard's president, Alan Garber, said in a statement on Monday.

Massachusetts Institute of Technology (MIT) followed Harvard's lead on Monday and also rejected the Trump administration's demands.

Despite the criticism, Trump is standing fast. On Tuesday he took another strike against Harvard, threatening to revoke its tax-exempt status.

Universities, as well as many charities and religious groups, are exempted from paying federal income taxes. This valuable tax break, though, can be removed if the groups become involved in political activities or move away from their stated purposes.