The minister issued a statement on Monday after a parliamentary inquiry heard evidence from the original candidate selected to be the state's Senior Trade and Investment Commissioner to the Americas.
Jenny West, a former deputy secretary at government agency Investment NSW, told the inquiry she was offered the $500,000 job in August.
But she felt "so confused" and "shocked" in October when Investment NSW CEO Amy Brown told her she no longer had the three-year position in New York.
"Ms Brown said that the position - and this is a quote - 'will be a present for someone'," Ms West told to the inquiry.
The inquiry heard Ms West was told her appointment was rescinded because the government had decided trade commissioner roles would no longer be the remit of the public service.
Mr Barilaro was earlier this year named as the successful candidate after he resigned from parliament, before withdrawing from the job amid a political storm last month.
Mr Ayres categorically rejects "any suggestion I exerted political influence on the recruitment process".
"I did not say the job was to be a 'present' for anyone and I find that idea to be offensive," he said in a statement.
"All my actions have been to ensure the independence of the public service during this recruitment process.
"Amy Brown is and was the decision-maker for this role."
A spokesperson for Premier Dominic Perrottet said the appointment was a matter for Investment NSW.
"Advice provided by Investment NSW Chief Executive Amy Brown was that there was no suitable candidate for the role in the first round of recruitment. This was reaffirmed in her evidence on June 29," the spokesperson said in a statement.
Penny Sharpe, Labor's leader in the upper house, who sat on the committee inquiry, says the evidence points to "something really rotten at the core of what's happening NSW".
"The idea that these types of positions are being given out as presents to mates is something that the community hates," she told Sydney radio 2GB on Tuesday.
"It really is explosive and worrying evidence that we heard yesterday," and there were "so many questions" Mr Ayres needed to answer.
"His role throughout this entire process has been extremely murky," she said.
Ms Brown also had more questions to answer about the process in light of Ms West's evidence.
"Labor believes she should be stood down until the inquiry has finished," she said.
