The Reform UK leader said Mr Sunak does not "care" about British history in an attack over his decision to leave D-Day commemoration events early last week.
Mr Farage has insisted that he was referring to Mr Sunak's "class" rather than his heritage as the Southampton-born son of first-generation immigrants.
The PM told reporters during an election campaign visit in West Sussex that his rival's remarks viewed by some as a racist dog whistle - were bad for the nation.
He said: "I'm not going to get involved in that because I don't think it's good for our politics or indeed our country." And the PM warned that voting for the arch-Brexiteer would result in Sir Keir Starmer entering No10.
Speaking to the BBC as part of its Panorama interviews with Nick Robinson, Mr Sunak said: "On July 5 there is only going to be one person that's Prime Minister and it's Keir Starmer or myself.
"A vote for anyone who is not a Conservative candidate is just making it more likely that Keir Starmer is that person." Mr Farage has said support for Reform UK is nearing an electoral tipping point for the Tories.
He claimed that Conservative candidates were "slowly but surely waking up and smelling the coffee" about the threat his party would pose in the General Election.
During a press conference he said: "They are realising that many of their longest-term and as they would have seen it - most loyal supporters say, 'Enough is enough"." He also reiterated his criticism of Mr Sunak's decision to leave D-Day commemorations early, saying it had gone down "very badly" with voters.
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