BP CEO Robert Dudley is warning that high oil prices could hurt the economic recovery in the U.S. and other nations.

His warning comes amid an intensifying presidential campaign season in which the health of the economy will play a major role in President Obama’s reelection prospects.

Reuters reported Tuesday on Dudley’s remarks to the World Petroleum Congress in Doha, Qatar, noting that he said, “we are probably walking a fine line” with respect to recovery and that the U.S. is especially vulnerable.