Putin served as president of the Russian Federation from 2000 to 2008, and has since served as Russia's prime minister while his protege, Dmitry Medvedev, took over as president.
While Putin said during his victory speech that some are hoping to destroy Russia, Dreier said America harbors no such ambitions.
"Contrary to what he said in his acceptance speech last night, we do not want to destroy Russia," Dreier said. "I believe that it is very important that we take every step that we can to encourage a strong, vibrant, growing, independent, democratic Russia."
Dreier also offered his "hearty congratulations" to Putin, despite reports of voting fraud that led to election protests early this week.
"Even though there have been reports from the Organization from Security and Cooperation in Europe of voting violations, we are where we are," Dreier said. "Vladimir Putin is going to be the next president of Russia."