Ms Arcuri is alleged to have had an affair with Mr Johnson while he was Mayor of London.
The American entrepreneur responded on Thursday to allegations made in The Sunday Times last weekend.
According to the newspaper, the businesswoman repeatedly told friends she shared an intimate relationship with Mr Johnson while was at City Hall.
The 34-year-old was speaking in Los Angeles, where she now lives.
The technology entrepreneur’s companies have received £126,000 in public money.
The prime minister is also accused of granting Ms Arcuri privileged access to three overseas trade trips led by him.
He has been accused of failing to declare a conflict of interest, but has denied any impropriety.
“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,” said Ms Arcuri.
“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.”
She added: “It’s such a shame to see successful business-women or just businesswomen in general, be persecuted.”
When she moved back to the US, the entrepreneur founded Hacker House, a company which was awarded £100,000 in public money earlier this year.
Mr Johnson has been referred to the police complaints body to assess whether he should face a criminal investigation over his links with the businesswoman.
A Department for Digital, Culture, Media and Sport investigation is under way into the £100,000 grant made to Hacker House.
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