WASHINGTON — For more than a year, President Obama has resisted meeting one on one with President Vladimir V. Putin of Russia and only reluctantly taken a phone call, freezing out the Kremlin leader over his intervention in Ukraine in their own personal cold war.

But this month, the two leaders will be in the same city at the same time amid rising tension in Syria, and the White House is divided by a debate over whether they should meet to try to work out their differences before the tumult in the Middle East escalates even further.

The recent deployment of Russian weapons and equipment to Syria has brought to a head a conflict that has dominated the Obama administration since Mr. Putin’s return to the presidency, the choice between engaging with Russia and trying to isolate it. If Ukraine and Syria are the world’s two most significant conflict zones, then some officials argue that the solutions to both problems ultimately go through Moscow, making it necessary to talk. Others, however, worry that agreeing to meet would only play into Mr. Putin’s hands and reward an international bully.

Mr. Obama’s own instincts tend toward talking rather than not, as he has shown with both Iran and Cuba, longtime foes of the United States. But he has a chilly relationship with Mr. Putin and has been frustrated that past interactions have either proved fruitless or been exploited later by the Russians or both. And given the supercharged environment over his nuclear agreement with Iran, the idea of renewed diplomacy with another anti-American leader could prove volatile at home.