Thousands have marched against the Abbott government’s first budget, calling the prime minister a “liar” who is trying to divide society.

A Sydney rally against the Abbott government’s budget cuts 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 on Sunday, which organisers said attracted 10,000 people.

Demonstrators also gathered in Melbourne, Brisbane, Adelaide and Perth to rail against what they called harsh and unjust policy.

The resounding theme of the day was to question the prime minister’s political integrity.

“Liar, liar, budgie smugglers on fire”, “Abbott is a liar, throw him out”, “Phoney Tony” read the protesters’ hand-made signs.

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

In Sydney, the Australian Services Union’s NSW and ACT secretary Sally McManus said the prime minister wanted to abolish fairness, equality and checks and balances for big businesses.

“You’re a liar, a wrecker and a divider of our country,” she told the crowd.

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,” she told AAP.

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.

Greens deputy leader Adam Bandt said Mr Abbott lied “through his teeth” to win government and has delivered a budget for the wealthy at the expense of everyone else.

“It takes guts to stand up to the wealthy and raise the revenue to fund a caring society, but a coward takes the axe to the young, the sick and the poor,” Mr Bandt said.

In Adelaide, 5000 vocal protesters marched to the steps of state parliament to protest against the cuts.

In Brisbane, Adrian Skerritt, of the community protest group the Cloudland Collective, told crowds that whenever there were economic problems governments took money from workers and cut welfare for the poor.

“They say things like outsourcing, privatisation, marketisation, all these stupid economist words,” Mr Skerritt yelled to uproarious cheers and applause.

“They say these things are good for us. What a hideous lie.”