Senator Nash's chief of staff, Alastair Furnival, resigned on Friday, days after Fairfax Media revealed he had significant links to the junk food industry when he was involved in pulling down a healthy food star-rating website.

He and Senator Nash intervened to pull down the website, even though it was in development for two years and was approved by state and territory food ministers.

Labor ramped up its attack on Senator Nash on Saturday, with opposition health spokeswoman Catherine King calling on Senator Nash to explain her ''misleading'' statements to Parliament.

Last week, Senator Nash told the Senate that Mr Furnival had ''no connection whatsoever'' with lobbying outfit Australian Public Affairs. On Tuesday night, Senator Nash told the senator that Mr Furnival, in fact, had a ''shareholding'' in the firm.

However, company documents lodged with the corporate regulator indicate Mr Furnival is, in fact, the co-owner of the company, through a parent company, Strategic Issues Management, which he owns with his wife, Tracey Cain.

Fairfax Media asked the offices of Senator Nash and Prime Minister Tony Abbott whether they were satisfied that Senator Nash had not breached the code of conduct.

A spokesman for Mr Abbott said only: ''This person has resigned from his position. That's the end of the matter.''

Senator Nash's office had no comment.

Ms King said the matter demanded ''an immediate explanation''.

"The question is, does the Prime Minister think these statements [to Parliament] are appropriate for his minister? And if he says yes, well, I disagree with him."

Asked whether she thought Senator Nash should resign, Ms King said: "I think that’s entirely a matter for the Prime Minister."

"The Prime Minister needs to clarify whether he believes there has been a prima facie breach of the Statement of Ministerial Standards by Senator Nash and clarify his office’s role in the employment of Senator Nash’s former chief of staff.

"If this conflict of interest was known, serious questions are raised about why this conflict was not resolved earlier," she said.

"Senator Nash must make a full explanation of what her knowledge of this conflict was and explain why she misled the Senate on multiple occasions.

"Senator Nash must also explain why she chose not to make reasonable inquiries as to whether this conflict had been resolved before she made no declaration to the ministerial council meeting she chaired in December last year."

Fairfax Media understands the Prime Minister's office was aware of Mr Furnival's connection with Australian Public Affairs but had expected him to divest himself of the shareholding.

- with Amy Corderoy, Mark Kenny