Washington DC police say four people have died during the storming of the Capitol building.
In addition to the woman shot by police, three others died as a result of “medical emergencies”.
So far, more than 52 people have been arrested – 47 of them for curfew violations.
The woman shot and killed during the storming of the Capitol was San Diego resident Ashli Babbitt. A US Air Force veteran, she is thought to have been shot after entering the building alongside other rioters.
US broadcaster Fox5 spoke to the woman’s mother-in-law who said Babbitt had been a Trump supporter.
She is thought to have been shot at around 15:00 Washington time, and was rushed to hospital but later pronounced dead.
The mayor of the US capital city has extended a public emergency for 15 days until after inauguration day.
“Many persons came to the District armed and for the purpose of engaging in violence and destruction and have engaged in violence and destruction. They have fired chemical irritants, bricks, bottles and guns,” Mayor Muriel Bowser said.
“Their motivation is ongoing.”
The declaration will allow the city to draw upon additional resources to protect residents, like enforcing curfews, expanding emergency services or distributing necessities.
The order lasts until 15:00 on 21 January, the day after Biden will be sworn in.
The city is already under curfew declared by the mayor from 18:00 on Wednesday to 06:00 (23:00 to 11:00 GMT), though dozens of people have been arrested for violating the order.
At the moment, we’re watching as lawmakers continue the process of certifying the Electoral College vote from the states. Biden won with 306 to Trump’s 232.
The number of votes is read out state by state.
If any objections are raised by both a member of the Senate and the House, then the lawmakers separate into their respective chambers and debate the matter for two hours before deciding whether or not to uphold it.
Global leaders have been expressing their shock over the attack in the US capital.
Canadian Prime Minister Justin Trudeau said “Canadians are deeply disturbed” by the “attack on democracy”.
Argentina’s President Alberto Fernandez expressed his support for Joe Biden and condemned the “serious acts of violence”.
President Ivan Duque of Colombia similarly rejected the violence and offered his support to members of Congress.
Chile’s President Sebastian Pinera condemned “the actions seeking to alter the democratic process”.