TOKYO, June 19 (Reuters) - Japan had more than 3 million visitors for a third straight month in May, official data showed on Wednesday, as the weak yen helped continue a record pace for inbound tourism.

The number of foreign visitors for business and leisure was 3.04 million last month, steady from the level in April, and down slightly from the all-time monthly record in March, data from the Japan National Tourism Organization (JNTO) showed.

Arrivals last month were up 60% from the same period last year and 9.6% higher than in May 2019. Japan had a record 31.9 million visitors in 2019 before the COVID-19 pandemic shut global borders.

The weak yen, languishing at a 34-year low against the dollar, is helping fuel a tourism boom in Japan. That's good news for the economy, with travellers spending a record 1.75 trillion yen ($11.1 billion) in the first quarter of 2024, according to the JNTO.

But the influx has raised concerns of "overtourism" at visitor hot spots. On Monday, the mayor of Himeji in western Japan floated the idea of charging foreigners three times the standard 1,000 yen fee to enter the city's famous samurai-era castle, the Asahi newspaper reported.

In explaining new trail fees to curb overcrowding on Japan's sacred Mt. Fuji, Yamanashi prefecture governor Kotaro Nagasaki told reporters this week the country should focus on attracting "higher spending visitors" over sheer masses of people.

Chinese travellers, previously the biggest contingent of Japanese tourists, are still about 30% lower than pre-pandemic levels. But travellers from other markets are picking up the slack, such as Indian visitors who reached a monthly record in May, JNTO data showed.

Dalia Feldman, marketing director for Tourist Japan, said her firm has seen an 11-fold increase in inquiries from India in the past year, while those from the United Arab Emirates are up almost eight fold.

"It appears it is the Japanese cuisine and natural sights that attract them the most," Feldman said. "Most of our Indian and UAE customers will ask to include some more food tours in their itinerary as well as external trips to remote and scenic areas."

($1 = 157.8200 yen) (Reporting by Rocky Swift; Editing by Eileen Soreng and Jacqueline Wong)