Asked repeatedly on an ITV programme on Monday morning whether she was having an affair with Johnson when he was Mayor, Arcuri refused to answer, reports the BBC.
"I am not going to be putting myself in a position for you to weaponise my answer," she said.
The businesswoman did confirm that he had visited her home - which was also her office - "five, 10, a handful of times", but added: "It's really not anyone's business what private life we had."
On the issue of trade missions, Arcuri told ITV that she had access because of the work she was doing - not because of any relationship with Johnson.
Arcuri said she had never discussed any sponsorship or grants with Johnson, and asked if he had helped with any "sponsorship money", she said: "Categorically no. Do you think I would waste his time talking about this stuff?"
Arcuri told ITV that the pair shared "a love" and "passion" for Shakespeare and literature during their friendship,
"Boris is extremely personable. He cares a lot about this country, and he cares a lot about people... he is a guy you want to hang out with."
Asked whether she ever loved Johnson, she said: "I've been asked that many times. And I care about him deeply as a friend, and we do share a very close bond, but I wish him well.
"I really do want him to focus on making Britain great again."
The allegations first emerged in the Sunday Times last month, with claims technology entrepreneur Arcuri had joined trade missions led by Johnson and received thousands of pounds in public money, the BBC reported.
The incumbent London Mayor, Sadiq Khan, has launched an investigation into the allegations at City Hall, and the Greater London Authority's Oversight Committee has given Johnson 14 days - ending this week - to explain his relationship.
Johnson has also been referred to the police watchdog, who will consider whether there were grounds to investigate the Prime Minister for the criminal offence of misconduct in public office.
( With inputs from IANS )