Sen. Rand Paul of Kentucky, a presidential hopeful and leading non-interventionist voice in the Republican Party, believes the United States should seek "respectful" relations with Russia and avoid antagonizing President Vladimir Putin over the ongoing political turmoil in Ukraine, where a Kremlin-backed government collapsed last week.

"Some on our side are so stuck in the Cold War era that they want to tweak Russia all the time and I don't think that is a good idea," Paul said on Tuesday, in an interview with The Washington Post.

Paul's comments underscore the latest foreign-policy fissure in the GOP, where the party's libertarian wing and Republican hawks have clashed over whether Putin is a threat and the future of U.S.-Russia relations.

In recent weeks, some Republicans, such as Sen. John McCain of Arizona, have encouraged President Obama to eventually welcome Ukraine into the North Atlantic Treaty Organization (NATO) and to pressure Putin and his allies to not meddle with Ukraine's government and internal politics.

"Watch out for Vladimir Putin because he will try to make mischief because he believes that Ukraine is part of Russia," McCain told CNN on Tuesday. "We ought to tell Putin that interference ... in the ways that he might do it, would be totally unacceptable to the United States."

Paul, however, said those recommendations are misguided, given the culture and history shared by Ukraine and Russia, and the damage such gestures could cause to U.S.-Russian relations.

"The Ukraine has a long history of either being part of the Soviet Union or within that sphere," he said. "I don't think it behooves us to tell the Ukraine what to do. I'm not excited about saying 'hey, let's put the Ukraine in NATO' to rub Russia's nose in it."

Republicans need to remember that Russia remains a geopolitical and military power, Paul added, and that hostile rhetoric has consequences.

"We still need to be conscious of the fact that Russia has intercontinental ballistic missiles," he said. "Though the Cold War is largely over, I think we need to have a respectful - sometimes adversarial - but a respectful relationship with Russia."

"I think we should have trade and relations, criticize them if they have human rights violations," he said. "But for the most part, we should be very glad that we've gotten beyond such a tense situation that we're worried that any minute we could have a nuclear war. We ought to be, I think, proud of where we've gotten with that relationship, and even when we have problems with Russia, realize that we're in a much better place than we were once upon a time."

Paul's distancing from the GOP's hawk bloc is part of a larger critique he has made of the party's approach to foreign and national security policy over the past year, from his criticism of the Obama administration's drone attacks to his opposition to the National Security Agency's surveillance.

In January, Paul gave a speech at the Center for National Interest, where he argued for more diplomacy with U.S. rivals, regardless of past tensions.

"I believe the answers to most problems that confront us around the world can and should be approached by engaging both friend and foe in dialogue," he said. "No, I don't naively think that dialogue always works, but I believe we should avoid the rigidity of saying that dialogue never works."