By Samuel Indyk and Rocky Swift

LONDON, Aug 12 (Reuters) - Global stocks held on to gains on Wednesday after U.S. inflation data came in as expected, while oil prices edged higher after a senior Iranian official told Reuters there were no discussions with Washington on extending a ceasefire.

The Consumer Price Index edged up 0.1% last month after dropping 0.4% in June, in line with a Reuters poll of economists and analysts. Annual CPI inflation slowed to 3.4% from 3.5% a month earlier.

"Inflation is heading in the right direction for now, and given Federal Reserve Chair Kevin Warsh’s desire not to give much, if any, forward guidance, there should be a fairly sanguine market reaction to these latest figures," said Richard Carter, head of fixed interest research at Quilter Cheviot.

Traders stuck to their bets that narrowly favour an interest rate hold at next month's meeting following the data, with markets giving about a 55% chance that the Fed will keep its policy rate in the current 3.50%-3.75% range. 

U.S. stock futures, the S&P 500 e-minis, were up 0.4%, holding onto gains after the data. Nasdaq futures rose 0.8%, as upbeat results from AI cloud company CoreWeave after Tuesday's close gave the AI trade another boost.  

In Europe, the pan-continental STOXX 600 was up about 0.2%. Major stock indexes in Frankfurt, Paris and London were up 0.1% to 0.4%. 

In Asia, stocks rose 0.9%, led by a 3.7% gain in South Korea's Kospi and an almost 1% rise in Japanese and Taiwanese stocks as chipmakers rose sharply. 

TALKS TO END IRAN WAR CONTINUE

Markets were still following negotiations to end the Iran war and reopen the Strait of Hormuz to shipping traffic. 

A senior Iranian source told Reuters there were no discussions between Iran and the U.S. to extend their ceasefire because, from Tehran's perspective, the deal had no start date and therefore there was nothing to extend. 

The update followed attacks on shipping in the Middle East on Tuesday, while both Iran and the U.S. have stepped up their rhetoric in recent days.

Despite the lack of progress, investors are calm, with stocks across the globe close to record highs.  

"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."

U.S. crude rose 0.7% to $83.71 a barrel and Brent rose 0.3% to $89.19 per barrel, with both poised to extend five-day positive streaks. 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.

In currencies, the dollar index dipped to 99.69. The euro and sterling both ticked up after the U.S. inflation data. 

The yen strengthened 0.3% to 158.81 per dollar, but remained off last week's high of 155.20 after several suspected rounds of intervention.

Spot gold rose 1.4% to $4,428 an ounce, while spot silver jumped 2.9% to $66.47 an ounce. 

(Reporting by Samuel Indyk in London and Rocky Swift in Tokyo. Editing by Barbara Lewis and Mark Potter)

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