Global stock markets were predominantly higher on Tuesday, with U.S. futures also advancing, mirroring a rally that pushed Wall Street shares to near a record close. The positive trend followed gains in major U.S. indices on Monday.

In early European trading, key markets showed upward movement. Britain's FTSE 100 climbed 0.8%, France's CAC 40 rose by the same margin, and Germany's DAX was up 0.8%. U.S. futures for the S&P 500 advanced 0.3%, while the Dow Jones Industrial Average futures increased by 0.6%.

Asian markets experienced a mixed performance. Japan's Nikkei 225 surged 1.1%, surpassing the 70,000 level for the first time since early July. South Korea's Kospi, however, lost 0.9%. Technology stocks in the region saw volatility, with Japan's Advantest gaining 3.9% while SoftBank Group fell 3.1%. South Korea's Samsung Electronics dropped 1.5%, and SK Hynix slipped 3.7%.

Other Asian markets showed gains, with Hong Kong's Hang Seng climbing 1%, Australia's S&P/ASX 200 rising 0.6%, Taiwan's Taiex edging up 0.2%, and India's Sensex adding 0.7%. Markets in mainland China remained closed for a national holiday.

On Monday, the S&P 500 added 0.7% to approach its previous record high, the Dow Jones Industrial Average gained 0.2%, and the Nasdaq composite reached an all-time closing high with a 1.1% increase. Technology companies like Nvidia and Broadcom supported these gains. Despite challenges posed by rising oil prices and bond yields, expectations for strong corporate earnings have bolstered recent stock rallies ahead of the earnings season.

Oil prices saw a decline of over 1% early Tuesday. Brent crude, the international benchmark, fell 1.3% to $99.07 per barrel, dropping below the $100 mark but remaining significantly higher than late February levels. U.S. crude futures lost 1.7% to $87.91 per barrel.

Analysts attribute the easing upward pressure on oil prices to increased volumes crossing the Strait of Hormuz and recovering oil flows through Saudi Arabia's East-West pipeline. However, persistent tensions between the U.S. and Iran continue to influence market sentiment, contributing to price support. Strategists noted that while signs of recovery in Persian Gulf oil flows are emerging, the market remains apprehensive about potential supply disruptions.

In the bond market, U.S. Treasury yields were near multi-decade highs. The 10-year U.S. Treasury yield saw a slight ease to around 5.27%, after briefly surpassing 5.35%, a level not seen since 2002. Investors are seeking higher returns on government bonds amidst rising inflationary pressures, partly driven by energy shocks from the Iran conflict, and with the U.S. national debt exceeding $40 trillion.

The U.S. dollar strengthened against the Japanese yen, rising to 158.18 yen from 157.91 yen. The euro traded higher against the dollar, at $1.1238, up from $1.1223.