By James Glynn

SYDNEY--The Reserve Bank of Australia continues to warn that inflation remains materially above its target, with price pressures expected to mount further in the second quarter.

In the minutes of its June 15-16 policy meeting, released Tuesday, the central bank noted that labor costs pressure remained widespread. While consumer and business sentiment remained weak, the bank added that overall activity data suggested economic growth is cooling as expected.

"Inflation was still materially above the board's target and the staff's expectation remained for underlying inflation to increase in the second quarter," the minutes said.

The minutes suggested that the RBA hasn't yet called time on the tightening cycle, which has already seen three interest-rate increases this year.

Still, the fallout from tighter monetary policy and the impact of elevated oil prices meant that the economy might yet slow, easing the RBA's concerns about an excess of demand and shortfall in supply across the economy.

Although inflation eased in May as fuel prices cooled, underlying inflation continued to strengthen as businesses passed on higher costs stemming from the Middle East conflict.

The consumer-price index rose 4.0% over the 12 months through May, down from the 4.2% for the year through April and the 4.6% in March.

However, underlying inflation accelerated over the month with the trimmed mean measure of inflation edging higher to 3.6%, from 3.4% a month earlier.

The emergence of a potential path to resolution of the conflict in the Middle East was discussed by the RBA's policy setting board, but it observed that this was still at an early stage.

"Members agreed that even if the resolution proves enduring, global commodity supply constraints would take some time to resolve," the RBA said.

"It would take some time to assess the ultimate impact on the economy of the tightening in monetary policy since February but, at this stage, it appeared to be having broadly the expected effect," the bank added.

The RBA left the official cash rate on hold at 4.35% at the meeting.

Write to James Glynn at james.glynn@wsj.com