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April marked the first back-to-back fall in the core CPI since 1982.
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Core CPI rose just under 1 percent over the past year.
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The so-called core CPI fell in March for the first time since January 2010.
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Stripping out food and energy prices, the core CPI advanced the most since January.
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Flat housing costs and weak prices for apparel dampened the core CPI in August.
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May marked the first time that the core CPI has dropped for three consecutive months.
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The rises in both the headline and core CPI indexes were in line with expectations.
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Thirty-four of 37 economists believe cuts in mobile phone fees will push down the core CPI.
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Core CPI is a gauge of underlying inflation.
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We project that core CPI year-on-year may begin falling as early as April, given softening energy prices.
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Markets had expected core CPI to rise 0.1 per cent last month.
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The January consumer price index last week showed a pick-up in both headline and core CPI inflation.
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But a rise in rental costs after months of stagnation allowed the core CPI to move higher.
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A measure of that, known as owners'-equivalent rent, makes up 31 percent of the so-called core CPI.
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The so-called core CPI rose as healthcare costs jumped by the most in more than three years.
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The core CPI was boosted by increases in prices for apparel, airline tickets, healthcare and household furnishings.