The lead prosecutor in the impeachment trial of former US president Donald Trump said Tuesday his case was based on "cold, hard facts," and proceeded to present extensive video evidence that Trump incited violence on January 6.

The historic second impeachment trial of Trump began with debate on whether trying an ex-president is indeed constitutional.

"You will not be hearing extended lectures here from me because our case is based on cold, hard facts," lead House impeachment manager Jamie Raskin, a lawmaker from Maryland, told senators.

He dismissed the argument of Trump's lawyers that he should not be tried at all.

"Their argument is that if you commit an impeachable offense in your last few weeks in office, you do it with constitutional impunity. You get away with it," Raskin said.

"In other words, conduct that will be a high crime and misdemeanor in your first year as president and your second year as president and your third year as president, and for the vast majority of your fourth year as president, you can suddenly do in your last few weeks in office without facing any constitutional accountability at all," he said.

"This would create a brand new January exception to the constitution of the United States of America."

Raskin then presented a lengthy video montage of scenes from the January 6 storming of the Capitol by Trump supporters, after the former president gave a fiery speech urging them to contest Joe Biden's election victory.

The video footage included scenes from Trump's pre-riot speech, and then scenes of violence as his supporters broke into the Capitol.

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