About 500 people protested against changes to pensions and welfare payments and the Coalition government's strict new earn or learn policy for young people.

Rally organiser Ben Peelman said he was heartened by the big turnout at short notice.

He said people's anger about the budget was clear from social media.

"I've never seen so much political discourse and argument happening about one issue on Facebook," Mr Peelman said.

He urged the crowd to lobby Tasmanian senators to block the budget.

More anti-budget protests are being organised for June and July.

A protest against the planned deregulation of universities is also going ahead at the University of Tasmania on Wednesday.

The Hobart rally coincided with demonstrations in Melbourne, Brisbane, Adelaide, Sydney and Perth, organised to rail against what has been described as harsh and unjust policy.

The Sydney rally briefly turned ugly after riot police arrested 13 people.

Officers moved in to make the arrests after a small group of protesters sat on a main Sydney CBD road and refused to get up.

It was the only major flashpoint in the Sydney protest, which organisers said attracted 10,000 people.

The resounding theme of the day was to question the Prime Minister's political integrity.

Hand-made signs read "Liar, liar, budgie smugglers on fire", "Abbott is a liar, throw him out" and "Phoney Tony".

Many signs featured caricatures of the Prime Minister with huge ears and Pinocchio-style noses or with his famous red budgie smugglers on fire.

Australian Greens leader Christine Milne, who was among the masses, was struck by the upwelling of anger across the country at the budget.

"He's relying on the Senate caving in ... but we will not support these vicious cuts to young people, welfare recipients and the sick," Ms Milne said.

In Melbourne, more than 10,000 protesters jammed the city centre and caused traffic chaos to voice anger about federal cuts to health and education in Victoria.