Japanese visitors to Hawaii, the state’s biggest overseas market, should rebound to “normal” levels within a few months after a collapse following Japan’s March tsunami, according to Hawaiian Airlines.

“We expect them to be back to normal by the end of the summer,” Chief Executive Officer Mark Dunkerley of the carrier’s Honolulu-based parent Hawaiian Holdings Inc. said in an interview in Singapore yesterday. “We had quite a strong drop in March and the beginning of April, but in the month of May, bookings started coming back.”

Japan Airlines Co. also said yesterday that the Asian nation’s outbound tourism market was beginning to recover after holidaymakers canceled plans for trips following the March earthquake that left more than 23,000 dead or missing. Japanese visitor numbers to Hawaii fell 4 percent in the first four months of the year, compared with an 8 percent increase overall, according to the state’s tourism board.

Hawaiian began flying to Tokyo in November 2010, and it will add Osaka services next month, said Dunkerley, who is attending the International Air Transport Association annual general meeting. The carrier plans to add one or two more Asian routes in the next year as well, he said.

The potential for Hawaii to win visitors from China, the world’s most populous nation, is curtailed by visa requirements, Dunkerley said. Chinese tourists need to meet a U.S. consular official about three weeks before traveling in order to get a visa, he said.

“We’re inhibited by a U.S. visa regime that makes visiting the country quite difficult,” he said. “In an environment in which the U.S. has a balance of trade deficit, to handicap an industry that’s a net exporter like tourism is particularly unfortunate.”

South Korean traffic to Hawaii doubled when citizens were granted permission to visit the U.S. without obtaining visas, he said.