"What we've seen in the United States is terribly distressing - terribly concerning," he told reporters in Canberra.
Former prime minister Malcolm Turnbull said Mr Morrison's “mealy-mouthed” response to the riots had not gone far enough.
“It should have been stronger. I think Scott should have really condemned Trump’s actions,” he told Channel Nine’s Today Show.
“I mean at some point you have got to call a spade a spade. There is no point in being mealy-mouthed about this.”
Other world leaders including British Prime Minister Boris Johnson have directly laid blame for the riot on Donald Trump’s refusal to concede the election.
Mr Turnbull said he understood the reluctance of an Australian prime minister to comment on overseas political affairs - but stressed this was different.
“This was the President of the United States inciting a mob – many of whom were armed to attack and lay siege to the country’s Parliament. This is staggering stuff – it is an insurrection and sedition,” he said.
Mr Morrison on Thursday stopped short of criticising Mr Trump when questioned about his responsibility.
"It's not for me to offer commentary on other leaders," Mr Morrison said in Canberra.
"I don't do that out of respect for those nations. And that's where I'm going to leave that matter.”
In contrast, Mr Johnson has “unreservedly condemned” Donald Trump for inciting the dramatic assault on the Capitol.
“Insofar as he encouraged people to storm the Capitol and insofar as the President consistently cast doubt on the outcome of a free and fair election – I think that was completely wrong,” he told reporters at Downing Street.
"I think what President Trump has been saying about that is completely wrong and I unreservedly condemn encouraging people to behave in the disgraceful way they did in the Capitol."
Liberal MPs repeat Trump claims
The criticism comes after a number of Coalition MPs, including George Christensen and Craig Kelly, have repeatedly spread misleading claims about the United States election since November.
When asked, Mr Morrison stopped short of condemning those MPs.
“You know, Australia is a free country. There’s such a thing as freedom of speech in this country and that will continue,” he said.
Labor's legal affairs spokesperson Mark Dreyfus accused Mr Morrison of remaining silent while members of his government peddled "dangerous conspiracy theories".
"The cowardly silence has to end Mr Morrison," he tweeted.
"This isn't "free speech" it's the hand-picked member of your own government peddling dangerous conspiracy theories and justifying violence to overthrow democracy."
He pointed to a post overnight from Mr Kelly claiming Facebook censorship is a bigger threat to democracy than the Capitol riots and promoting conspiracy theories over who was responsible.
Victorian state Liberal MP Bernie Finn has also appeared to support false claims by Donald Trump about election fraud.
On his private Facebook page he said Mr Trump would make history by fighting off “a concerted effort by globalists, big corporations, big media, the Washington Establishment and the mad Left to improperly remove him from the Oval Office".
He said Mr Trump would "succumb to … Deep State forces — but not before exposing the massive corruption undermining the American political system".
Mr Finn has since posted that he did not support the events at the US Capitol.