A man walks past electronic boards displaying various Asian countries' stock price indexes outside a brokerage in Tokyo, Sept. 1, 2015. Reuters

Asian shares were mostly lower Tuesday morning, following U.S. stocks, after oil slumped 3 percent, dragging down energy companies and the industries that supply them. Japan's Nikkei 225 fell 0.3 percent, South Korea's KOSPI 0.5 percent and Singapore's STI 0.1 percent.

In the U.S. on Monday, the Dow Jones Industrial Average, Standard & Poor's 500 and Nasdaq composite all fell 0.1 percent to 0.2 percent. The Nasdaq was dragged by a 1.2 percent decline in Apple, the world's most valuable company, based on concerns that iPhone sales may fall for the first time next year.

Brent, the global crude oil benchmark, fell $1.27 to $36.62 while West Texas Intermediate, the U.S. benchmark, dropped $1.29 at $36.81. Oil, which was over $100 a barrel in mid-2014, fell below $40 a barrel two weeks ago after Saudi Arabia refused to reduce oil production. That -- plus factors like rising U.S. production, China's economic slowdown and the expectation that Iran could join the oil market as early as January after the lifting of economic sanctions -- could bring prices even lower, with some analysts predicting $32.50 a barrel, Reuters reported.

That, in turn, could force oil companies to shut down more wells, shelve more projects, implement more layoffs and put off more orders of equipment and other supplies.

“Whenever the weakness in oil regains market attention, it weighs on sentiment,” said Toshihiko Matsuno, chief strategist at SMBC Friend Securities Co. in Tokyo, as reported by Bloomberg. "The energy sector will continue to be a drag.”