"The stakes are very high with Trump" said Dmitri Trenin, head of the Carnegie Moscow Centre. "There may be opportunities that no one will have thought of but at the same time there may be risks that overshadow anything that can be gained."
The election of the populist billionaire and former reality-show star is perhaps the most bizarre chapter in a superpower relationship that's taken the world from the brink of nuclear war to periodic detentes over the last half-century.
If the president-elect fulfills even some of his campaign promises, a Trump presidency could be a game-changer for Putin in his quest to restore Russian international influence lost since the collapse of the Soviet Union.
During the campaign, Trump at times questioned the key Western security alliances that Russia has long opposed and tilted toward the Kremlin's position on issues like the Syrian civil war and the Russian annexation of Crimea from Ukraine in 2014.
He suggested sanctions imposed on Russia over the Ukraine crisis could be eased. Even before his policies become clear, Trump's startling victory could embolden Putin to be more assertive from the Middle East to his former-Soviet neighbourhood.
"This opens new possibilities for Russia," said Alexei Mukhin, head of the Centre for Political Information in Moscow. "It weakens the stance on sanctions and means a joint fight against Islamic State is possible."
The Russian ruble and stock markets gained, avoiding the declines that convulsed many other markets, as investors anticipated potential economic benefits from easing tensions - and possibly sanctions - even as oil prices dropped.
Like this year's Brexit vote, Trump's triumph is part of a populist wave sweeping developed nations - a trend that the Kremlin has embraced and encouraged.
The success of cyber-attacks that US intelligence blamed on Russia in hurting Hillary Clinton by exposing the inner workings of her campaign could make the Kremlin more aggressive in meddling in elections elsewhere. While the outgoing administration and Clinton had vowed retaliation against Russia - which denied any role - Trump rejected intelligence findings that Russia was behind the breaches of the Democratic National Committee.
DPA reported that German Chancellor Angela Merkel warned that Russia could use cyber-attacks to influence next year's vote there, where she faces a strong challenge.
"It's quite possible Merkel will be forced from office and we'll be very happy about that," said Sergei Markov, a political consultant to Putin's staff.
Throughout the US campaign, Putin publicly claimed to have no preferred candidate. But he did little to conceal his warmth for Trump and disdain for his opponent. Just what financial and other ties link Trump and his aides to Putin's Russia remain unclear.
Still, Russian officials expressed concern that Trump might find his efforts to warm relations with the Kremlin stymied by entrenched interests in the US opposed to a thaw, especially given how divisive the election was. Trump's views often put him into conflict with the Republican foreign policy establishment, including influential and outspoken senators like John McCain and Lindsey Graham, who may seek to rein in any rapprochement with Moscow.
Even the Russian Orthodox Church, which is close to the Kremlin, warned Wednesday against "euphoria" as it welcomed the vote result. "Time will tell what kind of president he will be, whether he will fulfill the promises he made during the campaign," said Metropolitan Illarion, a church spokesman, according to Interfax.
At an early-morning reception at the US ambassador's residence, the mood was restrained as the results came in. Many of the Russian guests expressed caution about just how much change the new administration might bring. "Trump won't be able make any sweeping changes as the establishment will rein him in," said Mukhin of the Centre for Political Information.
Some differences appeared during the campaign. Trump vowed to renegotiate or scrap the nuclear deal with Iran reached last year, an accord that Moscow supports.
Trump may find that it's harder to find agreement with Putin than he imagined, according to Fyodor Lukyanov, who heads a Kremlin foreign-policy advisory panel. "He really thinks that as a businessman he can make better deals but the question is what will happen when he finds out that he can't," he said. "His disappointment may provoke irritation and everything could go in the opposite direction."
But for the moment, the outcome looks better than even the Kremlin could have expected. As recently as yesterday, state television had been highlighting the possibility that vote irregularities could rob Trump of victory. That issue disappeared from coverage.
"Only pluses, not a single minus," was how Vladimir Zhirinovsky, the firebrand leader of a pro-Kremlin nationalist party, described the vote result for Russia to state TV.
- Bloomberg