Mr Bolton admitted on Good Morning Britain (GMB) that the couple’s relationship was “obviously quite incompatible” with his position as party chief.
The Mail On Sunday printed texts it said had been sent by Ms Marney, including use of the word “Negro” and a message reading “This is Britain, not Africa” during a discussion about the royal engagement.
Mr Bolton said he would continue to support the family of Ms Marney, who had been left “distraught” by the revelations – but refused to resign as Ukip leader.
He said: “I don’t defend these comments whatsoever and indeed Jo has been suspended pending an investigation under the normal rules of the party for such things and it is against the constitution for the party to be racist in any way.
“As of last night the romantic side of our relationship is ended.”
Making it clear he wanted to stay in place as the party leader, Mr Bolton insisted “there are a great many people who fully support me”.
Asked if his position as leader had become untenable, he added: “First of all, I am not intending to resign – at all.
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“This will be a question for the party so it’s up to the party what happens in relation to my leadership, I’m not going to resign.”
Mr Bolton admitted he had talked about immigration with Ms Marney but claimed it was about “straightforward, mild things” such as points systems, but “nothing of this sort”.
He said he had been with her for four days when her messages were revealed, and had “no idea” about her reported views.
Despite ending their relationship, Mr Bolton said he would “stand by” Ms Marney, claiming his critics had used her to attack him.
He told BBC Radio 4’s Today: “One of the worrying aspects about this on a political level is that people have used Jo – and they have been able to, of course, because of her comments – in order to attack me.
“These are people who have tried in the past to attack me, have found no way of doing it, so now they are going at it through this.”
He added that “however appalling and insulting” the comments were “I honestly don’t believe that those are her core beliefs”.
Mr Bolton said his former girlfriend was “utterly devastated” by what had happened and maintained that the end of their relationship was “not a cold parting of the ways”.
Calls for Mr Bolton to quit earlier came from Ukip West Midlands MEP Bill Etheridge, who described the party leader as a “political lightweight”.
He said: “All we get day after day, despite the hard work of our activists, is talk about issues with his personal life, which, frankly, I don’t care about.
“But the way he is handling it is unprofessional.
“He’s a political lightweight, completely out of his depth and, frankly, he needs to move away.”
Former Ukip leadership candidate Ben Walker also called for Mr Bolton to resign, accusing him of having “deeply flawed judgment”.
The party’s National Executive Committee had already decided to meet next Sunday to discuss the controversy surrounding Mr Bolton.
In a statement to the Mail On Sunday Ms Marney, who describes herself on her Twitter profile as a model, actor and journalist, as well as a Brexiteer, apologised.
She said: “The opinions I expressed were deliberately exaggerated in order to make a point and have, to an extent, been taken out of context. Yet I fully recognise the offence they have caused.”
Mr Bolton left his wife Tatiana, 42, who gave birth to their second daughter at London’s St Pancras station in 2016 after going into labour on a train, prior to his relationship with Ms Marney becoming public in early January.