Police in Washington DC have made 68 arrests related to the violent storming of the US Capitol yesterday.

The city's police chief said: "We still have a significant amount of work ahead of us to identify and hold each and everyone of the violent mob accountable for their actions." 

The first round of Trump's supporters are due in court to face charges over the protests, as police stepped up their search for others involved in the violence.

Metropolitan Police Department Chief Robert Contee said 47 of the arrests to date were related to violations of Mayor Muriel Bowser's curfew, with 26 of those involving people arrested on US Capitol grounds.

Several others were arrested on charges related to carrying unlicensed or prohibited firearms.

Chief Contee told reporters last night that two pipe bombs were recovered from the headquarters of the Republican and Democratic national committees, as well as a cooler from a vehicle on US Capitol grounds that contained petrol bombs.

A total of four people died yesterday during the chaos at the Capitol, including one woman who was shot by a Capitol Police officer.

Chief Contee declined to identify the woman, saying next-of-kin notification was still pending.

Three other people died because of medical emergencies, he added, and 14 police officers were injured - two of whom remained hospitalised.

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It was not clear whether other federal or local police agencies, including the Capitol Police, had made additional arrests.

While the number of people arrested is expected to grow, the initial number paled in comparison with the more than 300 people arrested by police following the 1 June protests in the District of Columbia related to the police killing of George Floyd.

In that incident, baton-swinging police and federal agents fired smoke canisters, flash-bang grenades and rubber bullets to drive protesters farther from the White House, enabling Donald Trump to walk across Lafayette Square and hold up a Bible in front of historic St John's Church.

While law enforcement officers were severely criticised for being too aggressive at Lafayette Square, however, the Capitol Police are now facing questions about why they did not do more to secure the Capitol and let many of the rioters later exit the building without arrests.

Mayor Bowser said police intend to ask the public for help in identifying rioters, many of whom posed for photos inside the Capitol and can be seen in viral videos on social media without masks.

"We will be on the lookout," she said. "Some of them, we think ... have to be held accountable for the carnage."

The FBI has also asked the public to submit tips, such as images, videos and other information, to help agents identify people who were "actively instigating violence."

Mayor Bowser also extended a public emergency declaration for 15 days, an action she said will allow her to restrict peoples' movements around the city if necessary.

President-elect Joe Biden is slated to take the oath of office on 20 January, 13 days from today.