US stock futures drifted lower on Thursday as the focus tentatively turned back to the economy and the monthly jobs report, as worries over the Middle East conflict rumbled in the background.

S&P 500 futures (ES=F) dropped 0.3%, while contracts on the Dow Jones Industrial Average (YM=F) and the tech-heavy Nasdaq 100 (NQ=F) moved roughly 0.4% lower. All three gauges closed Wednesday slightly above the flatline.

Some calm has returned to a market rattled by escalating Mideast tensions that have driven sharp gains in oil prices. Israel has yet to launch its promised retaliation to Iran's missile strike on Tuesday, amid efforts by Western and regional leaders to stabilize the situation.

Investors are now bracing for the highly anticipated September jobs report on Friday, after a surprise uptick in private payrolls came alongside signs the labor market is loosening up. In focus is whether the data reinforce the trend of steady cooling or show signs of cracks.

Any new signs of deterioration could prompt the Federal Reserve to follow up its 0.5% interest-rate cut last month with another jumbo move, despite policymakers' expectation of a 0.25% cut in November. Stocks soared in September as the market celebrated the central bank's aggressive pivot to easing.

Readings on weekly jobless claims and the services sector due Thursday will be weighed for more clues.

Meanwhile, the Israel-Iran crisis helped drive oil prices higher for a third day, another potential drag on economic activity. Brent crude (BZ=F) and West Texas Intermediate (CL=F) futures were both up over 2% on Thursday.

On the corporate front, Levi Strauss (LEVI) shares tumbled over 10% in premarket after the jeans giant posted a disappointing revenue forecast and said it is considering a sale of its Dockers brand. Tesla's (TSLA) stock continued to slide in the wake of downbeat delivery figures, as Reuters reported the EV maker has halted US online orders for its cheapest Model 3.

Brent crude (BZ=F) and West Texas Intermediate (CL=F) futures were both up more than 1% on Wednesday, with traders paying a premium amid the prospect of risks to supply from heightened Israel-Iran attacks.

In single stock moves, Tesla (TSLA) shares fell more than 3% as global deliveries rose in the third quarter but fell short of Wall Street estimates.

Meanwhile, Nike (NKE) shares slid more than 6% after the sports shoe giant withdrew its outlook for the year, having fallen short on first quarter revenue. "We have yet to turn the corner," its CFO told analysts on a conference call.

On the macroeconomic front, the latest data from ADP out Wednesday showed the private sector added 143,000 jobs in September, above economists' estimates for 125,000 and significantly higher than the 99,000 seen in August. The release follows mixed data around job openings and comes ahead of the crucial September jobs report on Friday as investors mull the Fed's interest rate-cutting path.

Read more: What the Fed rate cut means for bank accounts, CDs, loans, and credit cards