Politicians were forced to evacuate the building after Congress had begun certifying President-Elect Joe Biden’s election victory.
Australian Prime Minister Scott Morrison said the scenes were "very distressing" and condemned the "acts of violence".
"What we've seen in the United States is terribly distressing - terribly concerning," he told reporters in Canberra.
Scott Morrison hopes for 'stable transition' of power in US
"This is a very distressing time in the United States and I feel terribly for what's happening there I really do."
The demonstrations are believed to have been inflamed by Mr Trump's false claims of a “stolen” election.
But Mr Morrison would not be drawn on criticising the sitting president when questioned about his responsibility for the unrest.
"We hope for a peaceful and stable transition of government to the new administration, elected by the American people," he said.
British Prime Minister Boris Johnson said the siege on the Capitol was “disgraceful” and called for the election result to be respected.
New Zealand Prime Minister Jacinda Ardern said she was "devastated" by the events.
Ms Ardern added that the right of people to exercise a vote should never be "undone by a mob".
"What is happening is wrong," she tweeted.
Mr Trump had earlier called on his followers to protest the certification of Mr Biden’s election victory.
Police drew guns as protesters tried to break into the House Chamber at the US Capitol with tear gas used to clear protesters from the building.
A woman died after being shot, Washington police have confirmed.
French President Emmanuel Macron said the scenes of supporters of the outgoing president taking up arms undermined the principles of democracy.
"What happened in Washington DC is not America, definitely," he said.
Canadian Prime Minister Justin Trudeau added that violence would "never succeed in overruling the will of the people."
"Democracy in the US must be upheld - and it will be," he tweeted.
Source: Chris Kleponis/Sipa USA
German chancellor Angela Merkel also criticised President Trump's refusal to concede the election.
"These images made me angry and also sad," Ms Merkel told a meeting of conservatives.
“I deeply regret that President Trump has not conceded defeat since November, and again refused to do so yesterday."
Scotland’s First Minister Nicola Sturgeon added that the scenes were “utterly horrifying” and shameful.
In response to the protests, president of the EU Commission Ursula von der Leyen tweeted "peaceful transition of power is at the core" of democracy.
NATO secretary-general Jens Stoltenberg also said the outcome of the election “must be respected”.
Former Australian leaders condemn 'mob violence'
Former Australian Prime Minister Malcolm Turnbull and Kevin Rudd have also expressed their concern, with Mr Turnbull directly blaming Mr Trump.
“The President should call on the mob he incited to disperse and go home,” he tweeted.
Mr Rudd said the protests were a “physical attack” on institutions of democracy by a “far-right mob”.
“All because of extremist statements by political leaders attacking the legal results of a democratic election, echoed faithfully by a cancerous far-right media,” he tweeted. “This affects us all.”
Opposition leader Anthony Albanese also said the "violent insurrection" in Washington was an "assault on the rule of law and democracy".
"What’s happening in Washington DC is a tragedy for the great democracy that is the United States of America," he told reporters.
"There is no doubt that both the words and actions of Donald Trump have encouraged this activity - it is a real concern."
Anthony Albanese blames Donald Trump for US Capitol violence
President Trump later posted a video to Twitter calling on protesters to "go home in peace", but continued to repeat unfounded claims that Joe Biden's election win was the result of fraud.
Mr Biden said: "the scenes of chaos at the Capitol do not reflect the true America and do not reflect who we are".