PARIS — Laying out clear conditions, President Obama and Western allies opened a pathway for Russia to ease tensions in Ukraine on Thursday but pointedly warned Moscow it could face new sanctions within weeks if Vladimir Putin fails to go along.

The leaders, who were gathered in Brussels for a wealthy-nations summit, said the Russian president could avoid tougher penalties in part by recognizing the legitimacy of the new Ukrainian government and ending support for an insurgency in eastern cities that is widely believed to be backed by the Kremlin.

There was no mention of rolling back Russia’s annexation of the Ukrainian region of Crimea, which precipitated the European crisis.

“We are at a point where Mr. Putin has the chance to get back into a lane of international law,” Obama said during a news conference with British Prime Minister David Cameron.

But Obama also said the West “can’t simply allow drift” in Ukraine, where insurgents continue to clash with government forces in eastern cities.

From Brussels, Obama and other leaders jetted to France ahead of events marking Friday’s 70th anniversary of the D-Day Normandy invasion that paved the way for the Allied victory in World War II.