While oil prices have recently fallen on news that a peace deal between the U.S. and Iran could come, prices are still significantly higher than before the war.
The Minneapolis Fed President warned that persistently high inflation risks becoming embedded in consumer expectations, potentially forcing tougher policy action later.
Prices related to travel, recreation and food saw particularly steep increases, stretching Americans' wallets as they celebrate the unofficial start of summer.
Putin is expected to hold talks with Chinese leader Xi Jinping on Wednesday, with the long-stalled Power of Siberia 2 natural gas pipeline topping the agenda.