The statement came as calls for his ouster grew on Thursday and members of his administration quit in the wake of a tumultuous 24 hours in Washington that also saw lawmakers finally confirm incoming president Joe Biden's election victory.

Trump did not acknowledge his role in riling up his supporters with with baseless allegations of election fraud and encouraging them to march to the Capitol.

He promised a smooth transition to president-elect Joe Biden, who defeated him in November's presidential election.

However, in a message to his "wonderful supporters", Trump added: "I know you are disappointed but I also want you to know that our incredible journey is only just beginning."

The Democratic leaders in Congress, Nancy Pelosi and Chuck Schumer, demanded that Vice President Mike Pence remove Trump under the Constitution's 25th Amendment. The calls were echoed by a Republican governor, a Republican lawmaker and numerous House Democrats.

"If the vice president and Cabinet do not act, the Congress may be prepared to move forward with impeachment," Pelosi told a press conference. Trump was impeached in 2019, but the Senate cleared him of charges last year.

US Transportation Secretary Elaine Chao became the first Cabinet official to announce their resignation following the attack on the US Capitol. Chao, who is the wife of Senate Republican leader Mitch McConnell, said the "traumatic and entirely avoidable event" had "deeply troubled" her.

Deputy national security adviser Matt Pottinger quit following the resignations of multiple administration officials.

Late on Thursday, White House Press Secretary Kayleigh McEnany condemned the violence that took place on behalf of President Donald Trump and the entire White House.

Trump had earlier issued a statement via his social media director saying there would be an orderly transition, the first time he made such comments since the election.

Social media giant Facebook banned Trump from his accounts indefinitely, citing his intent to "undermine the peaceful and lawful transition of power".

Twitter had locked Trump's account on Wednesday, though he was able to post from it nearly 24 hours later.

US lawmakers finally certified Biden's election win in the early hours of Thursday.

The joint session of Congress had been abruptly halted hours earlier after rioters breached both chambers of the Capitol building, forcing lawmakers to flee and hunker down until the siege ended.

One woman was shot and killed by Capitol police during the assault, the force said in a statement. Authorities said three others died in separate medical emergencies.

Police say they arrested 68 people.

US Acting Attorney General Jeffrey Rosen said some participants in the violence at the US Capitol would charged on Thursday and authorities would make more arrests in the coming days.

The Justice Department would ensure that "those responsible for this attack on our government and the rule of law face the full consequences of their actions under the law", he added.

The US Attorney's office, in conjunction with the Justice Department's counter-terrorism division, had so far charged 40 cases, officials said.

The majority of those deal with unlawful entry on the Capitol grounds, while a small handful are assault cases. Eight of the cases were also firearm cases.

Fifteen federal cases will also be filed later in the day on Thursday. One man was arrested by federal agents with a military semi-automatic rifle and 11 Molotov cocktails, according to officials at the Department of Justice.

Australian Associated Press