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Terror attacks against Paris and a Russian airliner, coming less than two weeks apart and both believed to be the work of ISIS, could trigger new cooperation between Russia and the United States.

Terrorists from the bloodthirsty caliphate in Syria and Iraq have been linked to both the downing of a Russian passenger jet over Sinai on Oct. 31 that killed 224 people, including at least 25 children, and a gun-and-explosives rampage in Paris that left 129 civilians dead and wounded about 350 more.

"It increases the chances of greater U.S.-Russian cooperation, since Moscow can provide the direct military engagement Washington is unwilling to provide," Donald Jensen, senior fellow at the Center for Transatlantic Relations.

"The Obama administration, though divided on how to deal with Russia, is likely to welcome greater Russian involvement on the ground and in the peace process. For the past few months, the U.S. has already eased its position on easing out Bashar al-Assad and including the Russians in the talks," Jensen said. President Barack Obama reiterated on Monday that the United States will not deploy significant numbers of ground forces in areas controlled by ISIS, which also goes by the name Islamic State.

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Omar Lamrani, military analyst at private intelligence firm Stratfor, said there has been an increased push by both Russia and the U.S. to work through their differences to deal with the common threat.

"The Russians have been seeking a strategic dialogue with the United States that diffuses the sanctions placed on them and normalizes the situation (including their gains in Crimea)," Lamrani said.

"Moscow will therefore push for increased cooperation with the U.S. against (Islamic State), but on their terms. The U.S. will be very hesitant to give that full recognition to Russia, but will be willing to work with the Russians on specific issues such as the fight against IS."

On Monday Obama, in Turkey for the G-20 summit, said without naming Russia specifically that there are disagreements with countries about the fate of Assad, whose strong-arm tactics are generally agreed to have triggered the Syrian civil war; however, he underscored that "what's different this time is that for the first time all major countries agree on a process that is needed to end this war."

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Some, though, remain only cautiously optimistic.

"I think it may force cooperation, but only the very lowest common denominator, mainly ensuring efforts in Syria don't actively undermine one another," the director of the Kennan Institute at the Wilson Center, Matthew Rojansky, told CNBC. "To the Kremlin, the main objective has always been to preserve what remains of its ally, Assad's regime, and that hasn't changed."

Eurasia Group President Ian Bremmer echoed those sentiments, saying that although Russia will focus more on ISIS given the recent attacks, Moscow's priority remains to "first shore up the Assad regime."

"We will see more effective efforts at deconflicting attacks and intelligence-sharing, but there's not enough trust or overlapping interest to bring the coalitions together," Bremmer said.

Moscow's Cosmos Hotel was evacuated the day after the attacks in Paris following a false bomb threat and just days after ISIS had vowed further revenge on Russia in a video "soon, very soon."

ISIS on Monday threatened attacks on Washington, D.C.

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Russia, no stranger to terror attacks in its own territory, now has to deal with a shift in which the Islamic Caucasus Emirate has also aligned itself with ISIS.

Monday's headlines in the Russian media highlighted that Russia is "ready to support the efforts of the armed opposition in Syria" and that the U.S. has called on Russia to join forces in the coalition to fight ISIS.

"Certainly I think the demands that Assad must go will to take a back seat to defeating ISIS in Syria," Helima Croft, CNBC contributor and global head of commodity strategy at RBC Capital Markets, told CNBC.

"No one is going to come out and say Assad must stay, but is policy going to shift more to the Russia position? I think so," Croft said.