WASHINGTON — Congressional Republicans face a vexing dilemma with the impending presidency of Donald J. Trump: Will they maintain the tough line on Russia that has been central to their foreign policy for decades, or cede that ground to Democrats?

For decades during the Cold War, Republicans tried to claim the hawkish mantle when it came to confronting the Soviet Union. Vice President Richard M. Nixon famously squared off against Premier Nikita Khrushchev in 1959, and years later President Ronald Reagan cast the Soviets as an “evil empire.”

Reagan made that kind assertiveness central to his foreign policy and he is credited by many with hastening the downfall of the Soviet Union, the most persistent and formidable adversary of the United States of the last 60 years. And Reagan disciples today in the Republican Party, including Vice President-elect Mike Pence, are many.

Reagan helped to frame the template for an American foreign policy that promulgated democracy around the world and curbed what has often been called Russian adventurism.