LONDON, Aug 12 (Reuters) - Global equity markets held steady and oil prices inched higher after new attacks on shipping in the Middle East dimmed expectations for an end to the Iran war, as markets turned their attention to U.S. inflation data later in the day. 

The U.S. and Yemen's Iran-aligned Houthis reported separate attacks on shipping, while both Iran and the U.S. have stepped up their rhetoric in recent days. Iran's top security official, Mohsen Rezaei, said on Tuesday that the vital Strait of Hormuz shipping route will remain closed unless the U.S. accepts Iran's conditions to end the war.

The war shows no signs of ending despite repeated claims from U.S. President Donald Trump of an imminent deal, threatening the global inflation and growth outlook as energy prices remain elevated.

U.S. crude rose 0.8% to $83.89 a barrel and Brent rose 0.7% to $89.49 per barrel, poised for a sixth straight daily gain. Both benchmarks settled more than $1 higher on Tuesday, marking their highest closes since July 31 and extending gains after jumping about 5% on Monday.

"Our base case for a long time has been a gradual but messy de-escalation," said Dorian Carrell, head of multi-asset income at Schroders.

"We don't expect traffic (through the Strait of Hormuz) to go to its full capacity. We think that puts a floor on the oil price and maintains an energy-driven inflationary driver in markets in the near- to medium-term."

In early European trade, the pan-region STOXX 600 was little changed. Major stock indexes in Frankfurt, Paris and London were hovering close to the unchanged mark. 

In Asia, stocks rose 0.7%, led by a 3.7% gain in South Korea's Kospi and an almost 1% rise in Japan and Taiwan stocks as chipmakers rose sharply. 

 U.S. stock futures, the S&P 500 e-minis, were up  0.1%, while Nasdaq futures rose 0.4%, as upbeat results from AI cloud company CoreWeave ( CRWV ) after the market gave the AI trade another boost.  

EYES ON CPI

Markets remained focused on U.S. consumer prices data later in the session for signals of timing for a potential Federal Reserve rate hike.

Wednesday's CPI data will not capture the most recent rise in energy costs, but it could still prove instrumental in setting expectations for the Fed's meeting next month, with money markets showing an even chance of a hike.

Consumer prices are expected to edge up 0.1% in July after falling 0.4% in June, according to a Reuters poll. Annual CPI inflation is forecast to slow to 3.4% from 3.5% a month earlier. 

"The CPI projection is expected to come in reasonably soft today which would tee up a hold before the midterms, all else being equal," said Schroders' Carrell.

Fed Bank of Boston President Susan Collins said she would back a September interest rate rise if inflation remains high, the Financial Times reported.

Markets are increasingly pricing in an early rate hike in Japan, putting pressure on the nation's shorter-dated bonds. The yield on the 5-year Japanese government bond rose to 2.12%, a record high, while the 2-year yield reached a 31-year peak of 1.645%.

Investors now price an almost 60% chance of a quarter-point hike at the Bank of Japan's September meeting. 

The yen weakened slightly to 159.35 per dollar, remaining off last week's high of 155.20 after several suspected rounds of intervention.

The dollar index, which measures the currency against a basket of currencies, rose less than 0.1% to 99.86. The euro and sterling were little changed.

Spot gold rose 1% to $4,409 an ounce, while spot silver rose 2% to $66.04 an ounce.