Mr Albanese called for Mr Morrison to contact Mr Trump and convey Australia’s strong view the democratic processes must be respected.
“That pressure needs to be bought by all people who believe in democratic processes,” the Labor leader said on Friday.
“Scott Morrison, as a democratically elected leader, has a responsibility to support democracy.”
Greens leader Adam Bandt said if the kind of behaviour shown by Mr Trump was happening in any other country, Australia would be intervening.
“Australians are watching in horror, the world is watching in horror and Scott Morrison is silent on Donald Trump’s dangerous, anti-democratic lies,” he said.
Mr Morrison’s office declined to comment. On Thursday, he said he had great confidence in the US democracy and its institutions and urged people to let the processes run their course.
Coalition MPs including George Christensen and Matt Canavan have made social media posts repeating claims similar to those made by Mr Trump.
Mr Christensen has posted more than a dozen times on Facebook since Wednesday evening alleging voter fraud, including links that have been fact checked as false by Facebook or attracted warnings that the information may be incorrect.
Mr Albanese said people spreading this kind of disinformation and conspiracy theories were undermining democracy.
“[Mr Morrison] has a responsibility to ensure that members of his caucus and his party behave responsibly at this time,” he said.
The Prime Minister’s office referred questions about the MPs to Foreign Minister Marise Payne, who has been working with international partners including the US to combat the spread of disinformation globally. Senator Payne and Deputy Prime Minister and Nationals leader Michael McCormack were asked for comment.
NSW Attorney-General Mark Speakman used Twitter to repudiate Mr Trump while the president was speaking.
“True conservatives defend civic institutions. True conservatives uphold public confidence in liberal democracy. True conservatives rely on facts, not manufactured alternative facts,” Mr Speakman said.
Katina Curtis is a political reporter for The Sydney Morning Herald and The Age, based at Parliament House in Canberra.