A second term does not necessarily mean a repeat of the first.
By most accounts, the Kremlin was hoping U.S. President Barack Obama would win a second term. His rival, former Massachusetts Governor Mitt Romney, declared during the campaign that Russia is the United States' leading "geopolitical foe."
By comparison, Putin sees the familiar Obama, analysts say, as more predictable and less enamored of U.S. international exceptionalism.
"I just recently was in Moscow talking to various people in government and outside the government who work in the foreign policy world and they certainly have been hoping that Obama would win because from their point of view he is the devil they know," Charles Grant, director of the Center for European Reform in London, says. "They don't like Obama that much -- they have a lot of problems with him in certain areas, like his plans for missile defense -- but they know what he stands for and, as one member of the Russian Duma said to me, he understands we are living in a multipolar world."
Now, the Kremlin has its wish, but that doesn't mean a return to the relatively warm relations of the "reset" of 2009 and 2010 is likely in the cards.
"The reset that Obama engineered with President Dmitry Medvedev has really come to an end," Grant says. "Since Putin became president for a third term, that sort of close rapprochement between Washington and Moscow has sort of evaporated, so I think there is more coolness than there was [before], even with Obama's victory."
During the brief reset, Washington and Moscow were able to sign the landmark START treaty, agree on four rounds of international sanctions on Iran, and generally reduce bilateral tensions that had soared at the end of George W. Bush's presidency. Now, however, harder issues remain on the table -- Afghanistan after the 2014 withdrawal of NATO-led combat forces, Iran, U.S. missile-defense plans, and Syria.
"The low-hanging fruit has already been picked, so [cooperation] will be less substantial than before," Anders Aslund, a senior fellow at the Petersen Institute of International Economics in Washington, says. "And the Russian suspicions about missile defense -- rather Putin's suspicions about missile defense -- will be quite strong."
Although relations with Russia are not on the top of the new Obama administration's agenda, Andrew Kuchins, director of the Russia and Eurasia program at the Center for Strategic and International Studies in Washington, foresees a reassessment of past policies and a new road map for bilateral ties.
"The U.S.-Russian relationship [has] been in a difficult period and [it] will continue to be pretty difficult for the time period ahead," Kuchins says. "I think that the Obama administration will be conducting a review of their Russian policies and where it is going in the light of a number of different developments in the last year and a half or two years. And we'll just have to see where they come out with that."
Among the developments that could motivate this reconsideration, Kuchins includes differences over missile defense; Russia's reaction to the Arab Spring, especially to events in Syria; and legislative and presidential elections in Russia in 2011 and 2012 that were viewed in the West as undemocratic.
The keystone of the reset -- cooperation on establishing security in Afghanistan -- will likely continue. But as the expected withdrawal of NATO-led combat forces by the end of 2014 approaches, difficult-to-assuage tensions could surface even in this area, Kuchins says.
"The Russians will be supportive, for the most part, of our efforts in Afghanistan, but they -- like a lot of people around the world and a lot of people in the United States -- have questions about just what is the U.S. strategy in Afghanistan post-2014 and what kind of deployment of U.S. military and security forces would be in the region -- inside Afghanistan and outside of Afghanistan," Kuchins says. "And that, of course, is an area where there is possibility for significant disagreement between the United States and Russia."
Moscow has also opposed further economic sanctions against Iran over its disputed nuclear program, another issue that is likely to greatly complicate relations with Washington in the coming months.
Analyst Grant notes that U.S.-Russian relations are determined as much by who is in the Kremlin as they are by who is in the White House, and that Putin has turned a particularly enigmatic face to the United States in recent months.
"There is a kind of contradiction in Putin's attitude towards America," Grant says. "On the one hand, when he met Obama at the G20 in Mexico, I'm told he was very constructive and said he wanted to work with Obama. And certainly in meetings I've had with Russian leaders recently, they have been quiet, calm, and sober on the United States rather than rhetorically aggressive. On the other hand, you have the public rhetoric out of the Russian media, which is strongly anti-American."
He notes that Russian TV news tends to portray the United States in "a very negative light almost all the time."
The CSIS's Kuchins agrees, describing Obama as "pretty pragmatic in that regard."
He suggests that Obama is likely "to engage with international partners that he believes he can have success with and reach some agreements with."
"He was able to do that with Dmitry Medvedev in Russia several years ago," Kuchins says. "The prospects of doing that with Vladimir Putin in Russia are going to be more difficult."