U.S. crude oil supplies rose 2 million barrels to 341 million in the week that ended March 24, the highest since April 1999, the Energy Department reported last week. Supplies of crude oil, heating oil and diesel are also above the five-year average.

"We don't have any space for crude oil," said Bruce Kahler, a shipbroker with Lone Star, R.S. Platou in Houston. "It's hard to move it if there's no place to put it."

Royal Dutch Shell Plc hired an Aframax tanker to ship about 600,000 barrels of oil to the U.S. Gulf Coast from the Caribbean for a rate of WS 175 as measured in the industry standard Worldscale measure, according to Lone Star's daily report. That's down WS 15 points, or 8 percent.

Rates on the voyage have fallen 35 percent since March 16, according to Bloomberg data.