Julia Gillard, Australia’s former prime minister, has said Donald Trump’s mental health will be increasingly questioned if he continues his behaviour on Twitter.

The US president was criticised by both Democrats and Republicans last week for attacking MSNBC presenter Mika Brzezinski by describing her as "bleeding badly from a face-lift".

Days later, he was accused of encouraging violence against journalists for posting a mocked-up video of him beating up a man with CNN’s logo over his face.

His erratic tweets have prompted some in the US to question his mental stability.

“I know that some people in the US, some commentators are not proffering that analysis by way of insult, they’re actually saying it because they are genuinely concerned,” Ms Gillard told ABC’s Lateline.