Brent crude futures were down 79 cents, or 1%, at $77.66 a barrel at 1:24 p.m. EDT (1724 GMT). They touched their highest level in more than two months earlier in the session, Reuters reported.

U.S. West Texas Intermediate crude was down 94 cents, or 1.3%, at $72.90.

"Traders are very nervous about higher interest rates, which could kill demand very quickly," said Dennis Kissler, senior vice president of trading at BOK Financial, adding that some investors were also engaging in profit-taking after last week's gains.

Both benchmarks rose more than 4.5% last week after Saudi Arabia and Russia announced fresh output cuts bringing total reductions by the OPEC+ group to around 5 million barrels per day (bpd), or about 5% of global oil demand.

San Francisco Federal Reserve President Mary Daly on Monday repeated that she believes two more rate hikes this year will likely be needed to bring down inflation that is still too high, while Cleveland Fed President Loretta Mester also signaled more rate rises.

Higher interest rates could slow economic growth and reduce oil demand.

The U.S. Labor Department reported last Friday the smallest monthly job gain in two-and-a-half years along with strong wage growth. The data strengthened the likelihood that the Fed would raise interest rates at its meeting later this month.

Meanwhile, China's factory gate prices fell at the fastest pace in more than seven years in June, according to government data, indicating a slowdown in the recovery in the world's second-largest economy.

However, oil demand from China and developing countries, combined with OPEC+ supply cuts, is likely to keep the market tight in the second half of the year despite a sluggish global economy, the head of the International Energy Agency (IEA) said.