The oil market is well supplied, with inventories at record levels globally, and the market continues "to be a bit soft," but prices are getting a big boost from the dollar's fall, Exxon Mobil CEO and Chairman Rex Tillerson told CNBC Friday.

"Inventory levels are at historic highs levels — especially in the U.S.," Tillerson said. But "a foreign exchange effect" is keeping prices higher, despite the amount of oil available.

"If you put the price of oil, which is priced in dollars around the world, and if you look at what some of the currency effects are with the weak dollar — in our view that is contributing about $20-25 a barrel to the price," he said.

The weakness in the dollar is one of the key reasons for this year's move higher in commodities, analysts told Reuters. The greenback's weakness makes dollar-priced commodities like oil and gold more attractive as a physical hedge for investors, analysts said.

Analysts told CNBC higher oil prices and a weaker dollar could affect the global economy's fragile recovery.