Updates prices to afternoon trading

By Sinéad Carew and Nell Mackenzie

NEW YORK/LONDON July 14 (Reuters) - MSCI's global equities index advanced modestly on Tuesday after softer-than-expected U.S. inflation data and strong quarterly results from major banks, while oil prices rose for a second day as the U.S. and Iran continued to strike each other's facilities in the Middle East.

The U.S. Consumer Price Index increased by a lower-than-expected 3.5% in the 12 months through June after surging 4.2% in May. The index fell 0.4% on a monthly basis, largely due to the recent retreat in gasoline prices from multi-year highs as a fragile U.S.-Iran ceasefire took hold in June.

After surging 9% on Monday, oil's gains were more modest on Tuesday, as U.S. President Donald Trump backed away from a proposal to charge a 20% transit fee to guard the vital Strait of Hormuz waterway as part of the U.S.-Iran conflict. The U.S. has not been able to gain control of the strait, leading oil-market participants to push prices higher as supply remains constricted.

U.S. crude oil futures CLc1 settled up 1.5%, or $1.20, at $79.34 a barrel while Brent LCOc1 settled at $84.73 per barrel, up 1.7%, or $1.43 on the day after both hit a roughly one-month high earlier in the day.

Iran fired ballistic missiles at a U.S. air base in Jordan while the U.S. attacked Iranian targets for five hours in its third successive night of attacks.

Shares of big U.S. banks rallied following results that showed the major firms were boosted by strong trading revenue and corporate deal-making. JPMorgan Chase <JPM.N> reported a record quarterly profit, pushing its shares to an all-time high, while Goldman Sachs GS.N, Bank of America BAC.N and Citigroup C.N all exceeded Wall Street's profit estimates.

IBM IBM.N was the day's biggest loser, as shares fell 25% after warning that it would take a big earnings hit in the second quarter as it failed to keep pace with a shift in corporate spending from software to data-center infrastructure. The technology company was the biggest drag on the S&P 500 .SPX.

While equity traders for now shrugged off the latest Middle East hostilities, Tim Ghriskey, senior portfolio strategist at Ingalls & Snyder, said the war is still an overhang for the stock market.

"Right now the market is discounting this issue but it's lingering. It's dampening market strength from the very strong results we saw from financial companies," he said, adding that "the favorable CPI number we see could be very different next month given what we're seeing in the oil market."

As of 03:48 p.m. the Dow Jones Industrial Average .DJI was up 68.56 points , or 0.1 %, to 52,567.20 , the S&P 500 .SPX rose 32.94 points , or 0.44 %, to 7,549.54 and the Nasdaq Composite .IXIC rose 261.39 points , or 1 %, to 26,134.57 .

MSCI's gauge of stocks across the globe .MIWD00000PUS r ose 4.70 points , or 0.4 %, to 1,121.56 .

Earlier the pan-European STOXX 600 .STOXX index finished up 0.17%, recovering from losses of as much as 0.9% before the U.S. inflation data eased rate hike worries.

DOLLAR WEAKER AFTER INFLATION DATA

Federal Reserve Chair Kevin Warsh, in his first delivery of the central bank's semi-annual monetary policy report to Congress, said he is doubling down on the Fed's 2% inflation target and is just as committed to the Fed's employment mandate as he is to the inflation mandate that he has repeatedly emphasized since taking over the U.S. central bank.

In currencies, the dollar broadly weakened after the softer-than-expected U.S. inflation data tempered expectations for Fed policy tightening.

The dollar index =USD, which measures the greenback against a basket of currencies including the yen and the euro, fell 0.33% to 100.94 , with the euro EUR= up 0.35% at $ 1.1421 .

Against the Japanese yen JPY=, the dollar weakened 0.13% to 162.21 .

U.S. Treasury yields fell in response to the inflation data. The yield on benchmark U.S. 10-year notes US10YT=RR fell 2.26 basis points to 4.587%, from 4.61% late on Monday. The 30-year bond US30YT=RR yield fell 0.42 basis points to 5.0938%.

The 2-year note US2YT=RR yield, which typically moves in step with Fed interest rate expectations, fell 6.13 basis points to 4.202 %.

Among precious metals, spot gold XAU= rose 1.28% to $4,051.29 an ounce.