The recent rise in gasoline prices is driven by unrest in the Middle East and is therefore not something the Federal Reserve is in a position to tackle, a top Federal Reserve official said on Thursday.

"We don't have a magic wand, unfortunately," New York Federal Reserve Bank President William Dudley told a meeting in Fishkill, New York in response to an audience question.

Dudley said it was hard to get a read on the recent drop in commodity prices, but added he hoped it would persist.