In 2.53pm trading, the Standard & Poor's 500 Index added 0.1 per cent. The Dow moved lower as slides in shares of Walt Disney and those of Boeing, down 2.4 per cent and 1.9 per cent respectively, outweighed gains in shares of Chevron and those of Caterpillar, recently up 1.3 per cent and 1 per cent respectively.
Walt Disney shares fell after the company posted disappointing quarterly earnings.
"Although we think that Disney can probably grow faster than most of its peers in the long run because of its global studio and parks businesses, it is also more weighted down by tepid growth and longer-term margin compression at media networks," Brian Wieser, an analyst at Pivotal Research Group, wrote in a note, Bloomberg reported.
Energy stocks rose with the price of oil, gaining more 3 per cent, as a US Energy Information Administration report showed that domestic crude inventories dropped more than expected in the week to May 5.
To be sure, increases in US crude production remain a concern.
"Growing oil output in the US, which reached its highest level since August 2015, will remain a thorny issue for price bulls," Abhishek Kumar, senior energy analyst at Interfax Energy's Global Gas Analytics in London, told Reuters.
There were also mixed clues about the outlook for US interest rate increases.
While Federal Reserve Bank of Cleveland President Loretta Mester on Monday warned against complacency towards raising rates, Dallas Fed President Robert Kaplan was more cautious.
"I still believe the base case for removal of accommodation is three times this year, but I'm very cognizant of the fact that inflation pressures have been more muted," Kaplan told reporters after an event at the Bush Institute in Dallas, Reuters reported. "There's no question that the path toward 2-per cent inflation has been slow and uneven."
In Europe the Stoxx 600 Index finished the day with a 0.2 per cent advance from the previous close. France's CAC40 Index gained 0.1 per cent, as did Germany's DAX Index, while the UK's FTSE 100 Index rose 0.6 per cent.