But the Labor leader, who is in the UK for the King's coronation, refused to reveal if he would be raising the imprisoned Australian's case during an upcoming visit from US President Joe Biden.
Assange has been in prison in the UK for more than four years and is fighting extradition to the US to face espionage charges.
"My position is that enough is enough. And I continue to say in private what I have said publicly ... that enough is enough," Mr Albanese told ABC TV on Thursday, UK time.
Asked if he would discuss Assange's case with Mr Biden, who is due to visit Australia for the Quad meeting this month, the prime minister said he wouldn't publicly foreshadow any discussions he planned to have with the US president.
"I can't do more than make very clear what my position is and the US administration is certainly very aware of what the Australian government's position is," he said.
Mr Albanese said Assange's case needed to be looked at in the context of the time the WikiLeaks founder had already spent in custody, comparing his treatment to that of Chelsea Manning.
The former US Army soldier was released in 2017 after disclosing hundreds of thousands of sensitive documents to WikiLeaks.
"When Australians look at the circumstances, look at the fact that a person who released the information is walking freely now having served some time in incarceration ... then they will see a disconnect there," Mr Albanese said.
"There is nothing to be served by his ongoing incarceration and I am concerned about Mr Assange's mental health."
Last month, Australian parliamentarians of all political persuasions - including several Labor backbenchers - signed a letter to US Attorney-General Merrick Garland urging him to end the pursuit of Assange.
The Australian has appealed to the UK High Court and the European Court of Human Rights to block his extradition.
In 2021 a British judge ruled Assange should not be extradited to the US due to concerns for his mental health, but the decision was overturned on appeal.