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.