Australia's prime minister has admitted that he made a mistake by winking with a smile in a talk radio studio while listening to a phone-sex worker complain about welfare cuts.

The gesture, captured by a television camera and broadcast prominently in national news bulletins, has proved an unwelcome distraction for Tony Abbott, who is selling unpopular budget cuts that are criticised as betraying his conservative government's lack of empathy for the poor.

A woman who identified herself as Gloria, a chronically-ill 67-year-old grandmother, called Australian Broadcasting Corporation radio in Melbourne yesterday to ask Mr Abbott how she was supposed to pay an extra 850 Australian dollars (£467) a year in medical expenses that she estimated the budget measures would cost her.

Mr Abbott winked and smiled after she told him that she survived on a pension and worked for a phone sex service "to make ends meet".

He later explained that he had been reacting to a smile from the show's host, Jon Faine, varying from the prime minister's office's explanation that he had been signalling to a producer that he was willing to answer the question rather than have the call cut short.

"Obviously it was an interesting call from someone who had an interesting story," Mr Abbott told Perth radio station 6PR later.

But after a storm of criticism on social media and from political opponents, the PM conceded that he made a mistake.

"I shouldn't have done it. I should have been more focused on the caller and less focused on the interviewer," Mr Abbott told the Nine Network television.

"Mistakes are always regrettable ... and I will do my best having made a mistake yesterday to make none today."

A woman identifying herself as Gloria called ABC again today, condemning Mr Abbott's wink as "slimy" and "sleazy".

It was a sentiment shared by Sarah Hanson-Young, a senator for the minor Greens party, which has vowed to block some of the government toughest budget measures.

"Rather than taking seriously her concerns of poverty and illness, he gave a wink and a smirk, and all I have to say to the prime minister on this is, 'What a creep. What a total creep'," she said.

After Mr Abbott acknowledged his mistake, Ms Hanson-Young called for him to stand down as his government's minister for women. Mr Abbott refused.

The criticisms come as opinion polls showed this week that Mr Abbott's eight-month-old coalition government is now less popular among voters than the centre-left Labor Party opposition.

The government's popularity plummeted after the release last week of the least popular deficit-cutting budget that Australia has seen in at least 18 years.

Hundreds of students protested around Australia yesterday over government plans to deregulate university fees, a measure expected to make tuition fees rise.