Prime Minister Tony Abbott has again brushed off claims his assistant health minister failed to act on a conflict of interest involving a staffer.

Prime Minister Tony Abbott continues to stand by Assistant Health Minister Fiona Nash after a Senate committee grilled her for more than three hours about a former staffer’s links to a lobbying firm.

“This is not so much a storm in a teacup, it’s not even a zephyr in a thimble – it’s nothing,” he told parliament on Wednesday after being quizzed by Labor MPs.

Senator Nash had earlier fended off claims she knew about a conflict of interest involving her chief of staff Alastair Furnival, who resigned after failing to divest his interest in Australian Public Affairs (APA) which has clients in the food industry.

She became engulfed in the controversy after it was revealed Mr Furnival had ordered the removal of a health department healthy food-rating website leading to claims he had a conflict of interest in the decision.

The senator said she knew of Mr Furnival’s links to the food industry, but had assurances he had divested himself of any conflict of interest.

“I had a series of undertakings put in place so that there could be no real or perceived conflict of interest,” she told a Senate estimates hearing in Canberra.

However, she refused to table a letter in which Mr Furnival outlined his undertakings.

“I am not going to provide you with internal communications,” she told Labor Senator Penny Wong.

Opposition Leader Bill Shorten led an inquisition of Mr Abbott in question time, saying Senator Nash had failed to ensure Mr Furnival had shed his APA directorship and shareholding.

“Hasn’t the minister misled the parliament and failed in her responsibilities as a minister in your government?” he asked the prime minister.

Mr Abbott said no, and backed his minister “to the hilt”.

“I can assure members opposite that on this particular issue there is Labor smoke but no coalition fire.”

Mr Abbott told reporters earlier that Senator Nash’s decisions were “eminently justifiable” and rejected suggestions the minister offered her resignation over the issue.

During the Senate hearing, health department secretary Jane Halton angrily denied suggestions she had “moved on” the bureaucrat who had refused to take down a food ratings website when requested to do so by Mr Furnival.

She said reporting lines had simply been changed as planned before the website’s removal.

“To say there is no link – that is not true, but to say that this was a consequence is also not true.”

Senator Nash rejected claims she had misled the Senate when initially denying any connection between Mr Furnival and APA, but corrected her statement six hours later.

“I recognised that I did need to provide additional information … to ensure there was clarity around that,” she said.