Relations between Queensland Premier Annastacia Palaszczuk and Prime Minister Malcolm Turnbull have hit a new low with each side hurling insults on Sunday.

In a fierce outburst sparked by frustrations over the federal government’s response to Cyclone Debbie, Ms Palaszczuk labelled Mr Turnbull a “shallow thinker who doesn’t understand his job as Prime Minister”.

“All we’ve seen lately is a fly-in, fly-out Prime Minister who is espousing thought bubbles without any deep policy conversation,” Ms Palaszczuk told reporters.

During a press conference in Brisbane, she said she was “at breaking point” after things took a hostile turn following the devastating, week-long storm.

Turnbull assailed

It wasn’t the only attack the PM endured on Sunday.

The strong character assessment followed the publication of a column by Peta Credlin, the high-profile former chief of staff to Tony Abbott, who said Mr Turnbull had a “woman problem”.

Citing research in the Australian Electoral Study, which showed the Coalition’s support among women at the 2016 election was the lowest since the survey began in 1987, Ms Credlin said the Turnbull government had a problem with women “it must urgently address”.

“With more women in the population than men, more women coming through our schools and universities than ever before, this is an unacceptable reality for any political party claiming to represent mainstream modern Australia,” Ms Credlin wrote in the News Corp press.

“At present, the government has 76 members in the House of Representatives comprising 63 men, and only 13 women …

“If the polling trend continues, it’s likely it will head into opposition at the next election with the number of female lower house MPs in single digits.”

Queensland on the attack

Ms Palaszczuk said she was angry with a number of recent incidents, including the dispute over the release of disaster relief funding, the Prime Minister’s unannounced visit to Queensland last week, and the way he announced Brigadier Chris Field as the state recovery coordinator before she was able to tell the Queensland Disaster Management Group.

“I am at breaking point and I am sticking up for the people of this state,” Ms Palaszczuk said.

On the other side of town, Immigration Minister Peter Dutton swiped back, calling Ms Palaszczuk’s comments an “embarrassing outburst”.

“Premier Palaszczuk is a laughing stock around Australia,” he said.

Mr Turnbull returned fire in a post on his Facebook page on Sunday afternoon.

“Queenslanders will have been disappointed, but perhaps not surprised, to read Annastacia Palaszczuk’s bitter, personal and wildly inaccurate attack,” Mr Turnbull wrote.

He said it was hard to know what prompted it.

“It follows the heartbreaking loss and damage of Cyclone Debbie,” he said.

“As the Premier knows, the federal government is contributing around 75 per cent of the disaster recovery funding.

“The Queensland Premier welcomed our help – only a month ago praising me and the federal government assistance she received, saying ‘the level of cooperation is unprecedented’.

“This assistance to Queensland was not a one-off – over the last decade the federal government has spent $10.5 billion on disaster recovery, of which 85 per cent was spent in Queensland.”

Both Ms Palaszczuk and Mr Turnbull are expected to meet in Townsville on Monday at a public ceremony.

-with agencies