Oil prices continued to climb while Asian shares experienced mixed trading on Tuesday as renewed violence in the Iran conflict exacerbated market uncertainty. Brent crude rose 0.8% to $91.23 per barrel, following a 2.7% increase on Monday. U.S. benchmark crude also saw gains, up 1% at $86.62 per barrel.

The conflict has disrupted traffic in the Strait of Hormuz, a critical artery for global oil shipments, contributing to elevated prices for gasoline and other goods. This surge in energy costs has amplified existing inflation concerns, pushing prices further above the Federal Reserve's 2% target.

Higher energy prices present a complex challenge for the Federal Reserve's interest rate policy, potentially complicating efforts to cool inflation without harming the job market. The U.S. is set to release August jobs data later this week, following a July report that indicated a stall in job growth with employers cutting 23,000 positions. Revisions to previous months' data also showed a greater-than-expected loss of jobs.

In equity markets, Hong Kong's Hang Seng index fell 0.9%, while the Shanghai Composite remained nearly unchanged. Tokyo's Nikkei 225 and South Korea's Kospi saw modest gains, as did Taiwan's Taiex and India's Sensex. Australia's S&P/ASX 200 experienced a slight decline.

U.S. stock futures indicated a positive opening, though Wall Street closed August on a downbeat note. The S&P 500 index dropped 0.3%, the Dow Jones Industrial Average fell 0.7%, and the Nasdaq composite slipped 0.1% on Monday. Declines were widespread across most sectors, with notable exceptions in energy stocks such as Exxon Mobil and Chevron, which registered gains. Conversely, utility companies Edison International and PG&E saw significant drops following reports of potential legislation allowing insurers to sue over wildfire claims.

Treasury yields showed mixed movement. The yield on the two-year Treasury held steady, reflecting expectations about Federal Reserve actions. The 10-year Treasury yield saw a slight increase, nearing levels observed prior to a past intervention in the bond market by the Trump administration. The U.S. dollar strengthened against the Japanese yen, while the euro weakened slightly against the dollar.

This report incorporates contributions from AP Business Writers Alex Veiga, Damian Troise, and Michelle Chapman.