Many economists expect economic growth to slow in April-June due to inventory adjustments at manufacturers, and the minutes suggest there is some concern that price gains could slow as well.
"Some members, noting the fact that the April consumer price index for Tokyo had been relatively weak, said attention should be paid to what implications such weakness would have for nationwide prices," the minutes showed.
The core consumer price index (CPI) for Tokyo, which excludes fresh food but includes energy, rose an annual 0.4 percent in April, government data show. Data released shortly after the BOJ's May meeting showed Tokyo's core CPI slowed to a 0.2 percent annual gain.
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Data due on Friday are forecast to show Tokyo's core CPI rose an annual 0.1 percent in June, while nationwide core CPI is expected to be unchanged in May.
Bank of Japan Governor Haruhiko Kuroda and other board members have argued that inflation will start to pick up quickly from the autumn of this year as last year's tumble in oil prices falls out of the annual calculations.
However, economists outside the BOJ have long been skeptical that inflation will accelerate as quickly as the central bank hopes.
The BOJ has kept monetary policy stable since expanding stimulus in October last year to prevent slumping oil prices, and a subsequent slowdown in inflation, from delaying the achievement of its 2 percent inflation target.