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SALEM, N.H. - Vivek Ramaswamy argues that former Vice President Mike Pence and some of his other rivals for the GOP presidential nomination "feel threatened by my rise."

Pence and Ramaswamy have been feuding for nearly two weeks — and on Monday they nearly came face to face for the first time since their tense exchanges at the initial Republican presidential primary debate, a Fox News-hosted showdown in Milwaukee, Wisconsin, on Aug. 23.

The two candidates, along with fellow 2024 GOP White House contenders former Arkansas Gov. Asa Hutchinson and former Rep. Will Hurd of Texas, mingled with Republican officials, lawmakers, activists and voters and addressed the crowd at the Salem, New Hampshire, GOP's annual Labor Day picnic.

But Pence and Ramaswamy kept their distance, with the multi-millionaire biotech entrepreneur and first-time candidate glad handling with voters as Pence addressed the crowd and the former vice president departed for another campaign event before Ramaswamy took to the stage about a half an hour later.

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Pence blasts Ramaswamy at first debate

Former Vice President Mike Pence and biotech entrepreneur Vivek Ramaswamy square off at the first Republican presidential nomination debate, on August 23, 2023 in Milwaukee, Wisconsin (Fox News)

That wasn't the case at the first debate, when the two repeatedly clashed.

Discussing the economy, Pence referred to Ramaswamy as a "rookie" and emphasized that "now is not the time for on-the-job training."

Ramaswamy, in a separate exchange as he referred to Pence while addressing the audience, argued, "Do you want a super PAC puppet, or do you want a patriot who speaks the truth?"

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Pence is polling in the mid-single digits, along with many of his rivals for the nomination, far behind his two-time running mate, former President Donald Trump. Ramaswamy, who grabbed plenty of attention at the first debate as he repeatedly came under attack from Pence, former ambassador and former South Carolina Gov. Nikki Haley and former New Jersey Gov. Chris Christie, has seen his support rise in recent polling, and is rivaling Florida Gov. Ron DeSantis for second place in some surveys.

Since the debate, the 64-year-old Pence has continued to take aim at Ramaswamy on a number of issues, from the 38-year-old's tax proposal to Russian's war on Ukraine, to the Sept. 11, 2001 terrorist attacks. 

Ramaswamy has returned fire, suggesting the then-vice president missed an "historic opportunity" to promote voting reforms as he certified the 2020 election results on Jan. 6, 2021, amid the attack on the U.S. Capitol. Pence called Ramaswamy's suggestion "incoherent and unconstitutional."

The high-profile spat is more than just a generational dispute, it's proxy battle between the populist MAGA wing of the party and more traditional conservatives over the future of the GOP 

"He's good man, a good family man. But he's just wrong on foreign policy," Pence said of Ramaswamy on "Fox News Sunday" this past weekend. "I mean, the way he wants to let [Russian leader Vladimir] Putin keep what he's grabbed in Ukraine and make promises that Ukraine will never be in NATO, the way he's willing to walk away from Taiwan after 2028 and let China grab it." 

Ramaswamy, Pence, cross paths but don't face off at GOP Labor Day picnic in key presidential primary state

Biotech entrepreneur Vivek Ramaswamy, a 2024 Republican presidential candidate, takes a photo with a supporter at the Salem, New Hampshire GOP's annual Labor Day picnic, on Sept. 4, 2023 in Salem, N.H.  (Fox News - Paul Steinhauser)

Asked about the criticism, Ramaswamy stressed in a Fox News Digital interview on Monday, "If you listen to exactly what I've been saying, I've been consistent. Now I understand why they're doing it. They feel threatened by my rise."

"A lot of those statements have been badly distorted. But I'm actually very clear about where I stand. I just favor our ability to respectfully disagree without actually mischaracterizing the opponents' positions," Ramaswamy emphasized.

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But Ramaswamy deferred from taking a direct shot at Pence.

Asked later about Pence as he took questions from reporters, Ramaswamy said, "He's a good guy, and I wish him well in his life as a family man and continue to do whatever he does, what’s in store next for him. But that’s not a principal concern of mine."

And he reiterated "the fact that we're having real debates in this party, the division between the neoconservative foreign policy establishment and a new unapologetically nationalistic vision of how we advance American interests, that's good. I'm glad we've smoked that out."

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Pence, asked about his differences with Ramaswamy, told reporters on Monday that "elections are about choices, and I had differences with a number of people on that stage and with one person who wasn’t on that stage," as he referred to Trump, who skipped the first debate.

Ramaswamy, Pence, cross paths but don't face off at GOP Labor Day picnic in key presidential primary state

Former Vice President Mike Pence, a 2024 Republican presidential candidate, addresses the crowd at the Salem, New Hampshire GOP's annual Labor Day picnic, on Sept. 4, 2023 in Salem, N.H. (Fox News - Paul Steinhauser)

"I’m going to continue to lay out my vision for the Republican Party and for America, and I’m going to draw the contrasts so that at the end of the day, Republican voters here in New Hampshire and across America are going to know I’m the most consistent and most qualified and most tested conservative in this race," Pence emphasized.

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The Labor Day picnic in Salem was Ramaswamy's last event during a jam-packed, four-day swing through the state that holds the first primary and second overall contest in the GOP presidential nominating calendar.

Pence arrived in New Hampshire on Monday for a busy three days of campaigning, including a speech on Wednesday titled "Populism vs. Conservatism: Republicans' Time for Choosing."

Get the latest updates from the 2024 campaign trail, exclusive interviews and more at our Fox News Digital election hub