Former Florida Gov. Jeb Bush briefly touched on the incident during a campaign speech in Spartanburg, South Carolina, saying it was the very reason American leadership is needed in the world.
"We're living in a world rife with insecurity," Bush said. "Today was another example of it, where a Russian plane was shot down and a helicopter apparently shot down right behind it. And it's because America's leadership in the world is so necessary for peace and security."
Both Florida Sen. Marco Rubio and Kentucky Sen. Rand Paul, colleagues on the Senate Foreign Relations Committee, positioned their viewpoints as the best answer to the situation.
Paul released a statement highlighting how his foreign policy positions are distinct from most of his opponents in the GOP primary. The libertarian-leaning Republican in general strongly opposes foreign intervention, and clashed with Rubio in a recent presidential debate over the need to cut back military spending.
"The shooting down of a Russian fighter jet illustrates precisely why we need open lines of communication with Russia and should resist calls from some presidential candidates to isolate ourselves from discussions with our adversaries," Paul said. "In addition, those who are calling for a no-fly zone need to realize that shooting down other countries' fighter jets will be the result and a war between nuclear superpowers a possibility."
GOP candidate Carly Fiorina has in the past called for not talking to Putin at all as a way to deal with Russian aggression, and many of the candidates are calling for establishing a no-fly zone within Syria as a way to curtail the Assad regime and protect Syrians.
Rubio, who has been a proponent of more military spending, spoke about the situation in Turkey on Fox News on Tuesday, saying that despite concerns about the direction Turkey has been going, the country is still a NATO ally and the U.S. must come to its defense.
That means if Russia were to retaliate, NATO allies would be obligated to get involved, he said, emphasizing he's been predicting such a situation since he got to the Senate.
"It's the reason why I warned about having Russia in the Middle East," Rubio said. "I warned exactly, specifically, this could happen. That there could be an incident with Turkey, a NATO ally. That they could aggressively fly over their territory and be shot down."
Rubio said the key question for escalation is what Russia does next, and that depends on how the U.S. responds.
"If Russia believes that they can respond and retaliate against Turkey because NATO's not going to do anything about it, what they are basically doing is they are making the argument that NATO is no longer viable, that it is a feckless alliance," Rubio said. "So it's important for us to be clear that we will respond and defend Turkey if they come under assault from the Russians."
Despite Russian President Vladimir Putin being a "gangster and a criminal" in Rubio's estimation -- epithets Rubio has used for the leader in the past -- the senator predicted Putin would not risk escalating the situation if he believed the U.S. would support Turkey.
The downing of the jet is just the latest overseas incident to shake the 2016 race. In the wake of the terror attacks in Paris and the bombing of a Russian passenger plane by ISIS, candidates have increasingly been focusing on national security and their plans to defeat ISIS.
That has made the civil war in Syria -- where ISIS has a strong foothold -- an even bigger issue in the race, as Russian forces have continued to hit targets in Syria that the West say have no strategic value for ISIS.