"I will decline your offer to endorse a candidate," the retired four star general told a virtual event with Sydney's Lowy Institute, joking that "retired generals need to retire their tongues during election season".

But the former marine went on to detail several qualities he looks for, and which seem to be at odds with Trump's bare-knuckled political brand.

"What I would look for most in a leader is competence and compassion," he said.

"I would look to the character and competence of the leader, compassion, empathy with their people, all their people."

Mattis also cited former president Harry Truman's promise to be "the president of those who did not vote for him" -- a message that Democratic nominee Joe Biden has channelled in recent days, as he tries to win over undecided and swing voters.

Since resigning from office Mattis has drawn fierce criticism from Democrats for his perceived failure to criticise Trump, and for an insistence on dodging political questions despite being a former Trump political appointee.

Mattis did briefly break his silence last June, after US military personnel were used to quash largely peaceful protesters.

"Donald Trump is the first president in my lifetime who does not try to unite the American people -- does not even pretend to try. Instead he tries to divide us," he wrote in the Atlantic magazine.

"We are witnessing the consequences of three years of this deliberate effort. We are witnessing the consequences of three years without mature leadership."

With three weeks to go until the final day of voting and with millions of ballots already cast, Trump is trailing in national polls and in several battleground states.