Ms Arcuri, a technology entrepreneur and former model, said she had every right to go on overseas trade missions with Mr Johnson when he was London mayor.
"This is an orchestrated attack on me, absolutely," she told the Daily Mail in Los Angeles, where she now lives.
"I'm being used as collateral. All the allegations are false.
"I had every right to be on those trips as a legitimate businesswoman and stand by everything that happened because these allegations are completely false.
"Someone has gone to great lengths to put together a massive attack and I stand by the legitimacy of my business.
"I am in fact a legitimate businesswoman."
Ms Arcuri added that it was "such a shame to see successful businesswomen ... persecuted".
She added: "One of the things I've been surprised with is how much support there has been for me, despite these allegations, because women see through these attacks and they know the narrative."
In an interview with LBC radio this week, the Prime Minister suggested stories about him and Ms Arcuri had come to light because of his Government's stance on Brexit.
"There are quite a lot of well-meaning and highly intelligent people who basically think that that would be something they don't want to see, and I think that there is a concerted effort now to frustrate Brexit," he said.
Reports claimed that Ms Arcuri, an American who moved to London seven years ago, was given £126,000 in public money and was given privileged access to three foreign trade missions led by Mr Johnson during this time as London mayor.
But the Prime Minister, who was embraced by his partner, Carrie Symonds, after his leader's speech at the Tory Party Conference in Manchester on Wednesday, said "everything was done with complete propriety".
Mr Johnson has been referred to the police complaints body to assess whether he should face a criminal investigation over his links with the 34-year-old American.