Mr. Yen sees the Japanese currency's 30 percent slump since 2012 coming to an end.

Eisuke Sakakibara, a former vice finance minister, says the Bank of Japan's acceptance of the yen's drop — and the Federal Reserve's tolerance for dollar strength — are wearing thin. The yen weakened past 125 per greenback for the first time in more than 12 years this week. Sakakibara, 74, said that policy makers are unlikely to allow a decline below 130.

"That isn't desirable for Japan as it could be damaging to the economy," Sakakibara, who earned his nickname in the 1990s for his influence over the exchange rate, said in a June 1 interview. "There will be a level where the U.S. won't tolerate further dollar strength," either.