Sen. Lindsey Graham, a Republican from South Carolina, announced Monday he will seek the Republican nomination for president. (Photographer: Luke Sharrett/Bloomberg) (Luke Sharrett/Bloomberg)

Sen. Lindsey O. Graham (R-S.C.) launched his campaign for president Monday on the promise of a muscular national security strategy, hoisting his bitter rivalry with Sen. Rand Paul (R-Ky.) from the Senate chamber onto the 2016 campaign trail.

As he kicked off his long-anticipated presidential bid in his home town of Central, S.C., Graham never mentioned Paul by name. He didn’t have to. The two have been openly fighting for months.

“I want to be president to defeat the enemies that are trying to kill us,” Graham said. “Not just penalize them or criticize them or contain them, but defeat them.”

He later added, “The Obama administration and some of my colleagues in Congress have substituted wishful thinking for sound national security strategy.”

His fight with Paul is one of the many variables Graham confronts in his underdog bid. He has also been the target of criticism from some conservative activists who say he has been too liberal on domestic issues, such as his support for a comprehensive immigration overhaul. And he faces a long climb out of low-single-digit territory in polls.

In Central, S.C., Sen. Lindsey Graham (R-S.C.) outlined his support for entitlement reform, energy independence and a strong national defense. Here are key moments from his announcement that he is running for president in 2016. (AP)

Despite the many obstacles, Graham could prove problematic for the rest of the GOP field because his home state is South Carolina — which comes third, after Iowa and New Hampshire, in the nominating process. Even if he doesn’t win the South Carolina primary, a solid showing could steal votes from one or more of the front-runners at a critical moment in the campaign.

Graham is in lock step with most of the Republican field in emphasizing aggressive foreign policies amid rising concerns about the Islamic State and other terrorist threats. But his long-standing feud with Paul has stood out among his rivals for its length, its vigor and its bitterness.

Graham entered the race a day after the National Security Agency’s authority for bulk collection of telephone records expired as Paul used a Senate procedural tactic to run out the clock. Graham, like most Republicans running for president, disagreed sharply — and very publicly — with Paul’s move.

As Paul spoke about the issue on the Senate floor late last month, Graham rolled his eyes, attracting widespread attention — including the attention of the Paul team, which began tweeting footage of the eye-roll.

Last week, a pro-Paul super PAC released a professional-wrestling-style campaign video that attacked Graham, showing him in a sports car that bursts into flames.

Graham recently said in a cable news interview that Paul has “been more wrong than right” on foreign policy. In a separate television interview the same week, Paul called Republican hawks such as Graham and Sen. John McCain of Arizona “lapdogs” for President Obama on foreign policy.

The Graham and Paul campaigns did not respond to requests for comments on the rivalry, and both men have taken pains to say the feud isn’t personal — even as their comments edge increasingly in that direction.

WASHINGTON, DC - JUNE 01: Sen. Rand Paul (R-Ky.). (Photo by Chip Somodevilla/Getty Images) (Chip Somodevilla/Getty Images)

Paul was asked Monday on “The Laura Ingraham Show” whether he thinks Graham is running to stop the Kentuckian from advancing in South Carolina or to be a wall for former Florida governor Jeb Bush or Sen. Marco Rubio (R-Fla.).

“I don’t know, but I do think that there’s probably not a great deal of traction for someone who believes in censorship of the mail, believes that you shouldn’t get an attorney to represent you when you’re accused of a crime, believes in the indefinite detention of American citizens,” he said.

Graham, 59, has long been among the most outspoken critics of Obama’s foreign policy decisions. He has advocated more forceful military strategies in Iraq and Syria and criticized negotiations with Iran over its nuclear program.

Paul, 52, has railed against government surveillance he sees as overly intrusive and has warned that the United States should be extra cautious when weighing whether to get involved in overseas conflicts.

But what once looked like a nominating contest that would settle their simmering dispute has become a largely one-sided debate. Polls show Americans increasingly worried about terror threats and most GOP candidates have rushed to embrace the staunchly hawkish views espoused by Graham.

For Graham, this development has been the best possible scenario — and the worst. With most of the field adopting some version of his outlook, it has left him little room to distinguish himself from a crop of fresher, better-funded hopefuls with similar talking points.

Graham’s strategy to stand out: emphasizing his deep experience dealing with foreign affairs, from his time in the military to his many years of service on relevant congressional committees.

“I have more experience with our national security than any other candidate in this race. That includes you, Hillary,” he said Monday, jabbing at the Democratic front-runner, former secretary of state Hillary Rodham Clinton.

But his pitch doesn’t appear to be moving many Republican voters. Graham, who launched a presidential exploratory committee in January, is barely registering in public opinion polls.

Key strategists who worked in the presidential campaigns of McCain — Graham’s biggest champion and closest friend in the Senate and another foreign policy foe of Paul — are expected to steer Graham’s under­dog bid. Christian Ferry, who was deputy campaign manager for McCain in 2008, is expected to manage Graham’s campaign. Jon Seaton, a top political strategist for Graham, also worked for the Arizona senator.

The Graham team will need to counter skepticism among conservative activists over his position on immigration, his votes for Obama’s Supreme Court nominees and his criticism of the tea party movement.

Graham is a South Carolina native, a lifelong bachelor and an Air Force veteran. He worked his way up from the state House to the U.S. House in the 1990s. He was first elected to the Senate in 2002.

“For a guy like me, it’s pretty simple,” Graham recently told Time magazine. “I do well in Iowa and finish in the top tier in New Hampshire, I’ll win South Carolina. By the end of South Carolina there are three or four people left at the most.”

McCain has expressed confidence that Graham will perform well in debates. If Paul and Graham do end up in on a debate stage with each other, it could provide some of the biggest fireworks of the campaign.

“I don’t want to raise expectations, but I am confident in a debate he will make an impression on the American people,” McCain said this year.

Katie Zezima contributed to this report.