(CNN) - Five days ahead of his state's primary – an election in which he promises to remain neutral – former Florida Gov. Jeb Bush on Thursday cautioned the contenders to soften their assaults, avoid a "circular firing squad," and connect personally with swing voters in the most diverse primary yet.
"If we do nothing to try to reach out to voters that believe in our values but feel turned off by the rhetoric, that is the dumbest thing in the world to do," he said in an interview to air on CNN's "John King, USA," when asked if a breach is forming between Latino voters and the GOP.
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His warning to "not go over the top in his attacks" was primarily aimed at former House Speaker Newt Gingrich, who continued the sparring between himself and former Massachusetts Gov. Mitt Romney by calling his rival "grotesquely hypocritical." The jabs exchanged between the two leading contenders has only increased as the campaign moved to Florida, with the two-man jousting largely overshadowing attention paid to the two other candidates former Pennsylvania Sen. Rick Santorum and Texas Rep. Ron Paul.
"I think there's a point past which Republicans and independent voters get turned off by this fierce primary spilling over into personal attacks," he continued, adding "I would hope that both Gov. Romney and Speaker Gingrich would stay away from that."
Both his father and brother were former presidents, but Bush said that if he, too, had been interested in a White House run, this election season would have been the ripest. Earlier in January, former first lady Laura Bush said she wished Jeb, her brother-in-law, would run, saying, "We wanted him to this time."
"Never say never, but in all honesty, this was probably the right time for me, in terms of my age and just the opportunity that existed but there are personal and family reasons that made that impossible," Bush said in the interview. "I hope in 2016 I'll be working on the reelection of a Republican president."
He said he has both spoken with and emailed Romney to express his decision to remain neutral.
The field without him includes "well qualified candidates," Bush said, who must emphasize the relevancy of their messages to Florida's significant and swing Latino voters next Tuesday. He is co-chair of the Hispanic Leadership Network Conference, a co-sponsor of Thursday evening's debate on CNN.
"The growing populations in all of the swing states are Hispanic voters," he said. "This is an over-simplification, but I don't think a party can aspire to be the majority party if it's the old white guy party."
While his advice to Gingrich is to tone down the attacks, Bush suggested Romney should connect more personally with voters.
"His challenge is also to show his heart," he said of Romney "He has a great record, and he's been a successful man in every way, and I think people can relate to that if he expresses himself in the right way."
But Bush said he intends to endorse no candidate in the race, instead allowing one "earn" his victory.
"I've already voted, I voted absentee," he told John King, "and thank God it's a secret ballot, John."