By Sophie Kiderlin and Gregor Stuart Hunter

LONDON/SINGAPORE, July 8 (Reuters) - The U.S. dollar nudged lower on Wednesday as currency markets broadly shrugged off a fresh exchange of strikes between the U.S. and Iran, while New Zealand's currency jumped after the country's central bank lifted interest rates.

The U.S. dollar index, which measures the greenback's strength against a basket of six currencies, was down 0.2% at 100.97, after earlier reaching its highest since July 2.

On Wednesday, Iran's Revolutionary Guards said they attacked U.S. military sites in Bahrain and Kuwait after the U.S. launched a wave of airstrikes against Iran in response to attacks on tankers in the Strait of Hormuz.

Brent crude was last up 2.2% at $75.78 a barrel, extending a rally into a second day.

The greenback, widely considered a global safe haven, pared some earlier gains as the trading session progressed.

"There hasn't been a huge reaction in foreign exchange, and I think that fits because for the vast majority of this war, the market has taken a glass half-full approach," Jane Foley, head of FX strategy at Rabobank, said. 

"With respect to this latest skirmish, therefore, the natural progression of that frame of mind is to look through it and assume they will still start talking," she said. 

NEW ZEALAND HIKES, FED MINUTES IN FOCUS

Meanwhile, the kiwi dollar was 0.7% higher at $0.5719 after the Reserve Bank of New Zealand hiked rates by 25 basis points to 2.5% to curb inflation pressures, as most economists had expected, and said "some further reduction in monetary stimulus is likely to be required" to control inflation. 

"A key argument for the hike is a concern that financial conditions would have eased further if the OCR was left unchanged," Westpac analysts wrote in a research note, referring to the central bank's official cash rate.

Later in the day, traders will be watching out for minutes from the Federal Reserve's June meeting, which was new Chairman Kevin Warsh's first. 

"Today’s minutes will clarify how serious members are about the possibility of rate hikes," Francesco Pesole, FX strategist at ING, said in a note.

"Based on post-meeting communication, we see limited risk of a dovish surprise in the minutes. We expect a cementing of the hawkish message to firm up dollar momentum," he said, noting that a break higher was not expected, however, as markets may hesitate to re-rate expectations sharply higher after last week's soft jobs data.

Elsewhere, the U.S. dollar was a touch higher against the Japanese yen at 162.18 yen, advancing for a fourth day as traders remained alert to possible intervention from Japanese authorities. 

The euro was 0.15% higher at $1.1427, while the British pound was up 0.1% at $1.3366. 

(Reporting by Sophie Kiderlin in London and Gregor Stuart Hunter in Singapore; Editing by Stephen Coates, Kevin Buckland and Alex Richardson)

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