US senators have voted to move forward with Donald Trump's impeachment trial on a charge of inciting the deadly assault on the Capitol, rejecting a claim the proceeding was unconstitutional after viewing graphic video of the January attack.

The Senate voted 56-44 to proceed with its trial of the former president, a historic first, rejecting largely along party lines his defence lawyers' argument that a president cannot face trial after leaving the White House.

Democrats hope to disqualify Mr Trump from holding public office again.

The video presented by the team of nine House of Representatives Democrats showed Mr Trump's followers throwing down barriers and hitting police officers at the Capitol.

It also showed the moment when police guarding the House chamber fatally shot protester Ashli Babbitt. Five people including a police officer died in the rampage.

The video interspersed images of the Capitol violence with clips of Mr Trump's incendiary speech to a crowd of supporters moments earlier urging them to "fight like hell" to overturn his election defeat.

The mob attacked police, sent politicians scrambling for safety and interrupted the formal congressional certification of President Joe Biden's victory after Mr Trump had spent two months challenging the election results based on false claims of widespread voting fraud.

"If that's not an impeachment offense, then there is no such thing," Democratic congressman Jamie Raskin, who led the prosecution, told the assembled senators - serving as jurors - after showing the video.

In another scene, a rioter sifting through the contents of the desk of a politician can he heard saying, "There's got to be something here we can use against the scumbags."

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Trump impeachment trial: What to expect

Mr Trump was impeached by the Democratic-led House on 13 January on a charge of inciting an insurrection.

He appears likely to be acquitted thanks to support from fellow Republicans in the narrowly divided Senate.

Convicting him would require a two-thirds majority, meaning that at least 17 Republicans would need to join the Senate's 48 Democrats and two independents in voting against Mr Trump. That is a tall order.

Mr Trump is the only president to go on trial in the Senate after leaving office and the only one to be impeached twice.

The trial was held with extraordinary security around the Capitol in the wake of the siege including armed security forces and a perimeter of fencing and razor wire.

Mr Trump's defence has argued he was exercising his right to free speech under the Constitution's First Amendment when he addressed supporters before the Capitol attack.

"We can't possibly be suggesting that we punish people for political speech in this country," Bruce Castor, one of Mr Trump's lawyers, said as the defense team began its presentation.

"We are here," Mr Castor said, because the Democrats who control the House do not want to face Mr Trump as a political rival in the future and because Democrats fear that American voters will want Mr Trump back as president in 2024.

Mr Castor said the storming of the Capitol "should be denounced in the most vigorous terms" and the rioters should be prosecuted to the fullest extent possible - reflecting the defense contention that "a small group of criminals" - not Mr Trump - were responsible for the violence.

"Presidents can't inflame insurrection in their final weeks and then walk away like nothing happened. And yet that is the rule that President Trump asks you to adopt," Democratic congressman Joe Neguse told the senators.

Most of the senators at the trial were present in the Capitol on 6 January, when many politicians said they feared for their own safety.

Democrat Raskin wept as he recounted how relatives he brought to the Capitol that day to witness the election certification had to shelter in an office near the House floor, saying, "They thought they were going to die."

Mr Raskin said his 24-year-old daughter never wants to return to the building.

Republican Senator Bill Cassidy called the Democrats' speeches "a very good opening".

"The arguments they gave were strong arguments," said Mr Cassidy, one of the Republican senators who voted last month that a post-presidency impeachment trial would be unconstitutional.

Most legal experts have said it is constitutional to have an impeachment trial after an official has left office.

The trial could provide clues on the Republican Party's direction following Mr Trump's tumultuous four-year presidency.

Sharp divisions have emerged between Trump loyalists and those hoping to move the party in a new direction.

Meanwhile, Democrats are concerned the trial could impede Mr Biden's ability to swiftly advance an ambitious legislative agenda.

One year ago, the then-Republican-controlled Senate acquitted Mr Trump on charges of obstructing Congress and abuse of power for pressuring Ukraine to launch an investigation into Mr Biden and his son Hunter in 2019.