US President Donald Trump weighed in for the first time on the massive protests of his presidency in Washington and around the globe, stating sarcastically on Twitter that he was "under the impression that we just had an election!"

His tweet came in response to more than a million people gathering on Sunday for the Women's March on Washington and at other rallies in the United States and abroad, all meant as a rejoinder to his inauguration a day before. Trump and his aides remained silent about the protests yesterday.

"Watched protests yesterday but was under the impression that we just had an election! Why didn't these people vote?" Trump asked on Twitter.

"Celebs hurt cause badly," he said.

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The massive event in Washington, which organisers said drew as many as half a million people, was packed with celebrities, including Madonna, Amy Schumer, America Ferrera and Ashley Judd.

Later, Trump sent a more conciliatory tweet:

"Peaceful protests are a hallmark of our democracy," he said. "Even if I don't always agree, I recognise the rights of people to express their views."

In another tweet, Trump, who yesterday accused the media of under-reporting the crowd size at his swearing-in, boasted that the television ratings for his inaugural was higher than that of President Barack Obama's swearing in four years ago.

"Wow, television ratings just out: 31 million people watched the Inauguration, 11 million more than the very good ratings from 4 years ago!" Trump wrote.

Nielsen reported that 30.6 million viewers watched inaugural coverage.

That figure was lower than Obama's first inauguration in 2009, when 38 million viewers tuned in, according to Nielsen. The record is held by Ronald Reagan, when 42 million watched his inaugural festivities in 1981.