SINGAPORE, July 14 (Reuters) - Stocks swung between gains and losses and oil hit a one-month high in early Asian trading on Tuesday after President Donald Trump said the U.S. was reinstating its blockade of Iranian shipping in the Gulf and would collect a 20% fee on cargo traversing the Strait of Hormuz. 

In a volatile start to the session, MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.4%, led by a 2.2% gain for Korean shares. Japan's Nikkei 225 was up 0.2%, while S&P 500 e-mini futures nudged 0.1% lower.

Brent crude futures climbed 2.6% to $85.50 a barrel, their highest since mid-June, as trading resumed in Asia.

Markets were also rattled by hawkish comments on Monday from Federal Reserve Governor Christopher Waller, who said the U.S. central bank may need to raise interest rates "in the near term" if coming data show inflation continuing well above the 2% target.

"While the risk had been building in the system over the past week, markets reacted aggressively" to the latest headlines from the Iran conflict, said Chris Weston, head of research at Pepperstone Group Ltd in Melbourne.

"The prospect of tighter monetary policy into a potential energy shock is rarely supportive for risk assets."

Overnight, stocks on Wall Street sold off and oil futures surged more than 9% as conflict between the United States and Iran re-ignited, once again throttling the flow of goods through the Strait of Hormuz. The S&P 500 closed 0.8% lower and the Nasdaq Composite fell 1.6%.

U.S. CPI data is due for release later on Tuesday, followed by comments from Fed Chair Warsh, who will deliver the central bank's semi-annual monetary policy report to Congress.

Fed funds futures are pricing in an implied 43.3% probability of a 25-basis-point hike at the U.S. central bank's next two-day meeting on July 28-29, compared to a 34.2% chance on Friday, according to the CME Group's FedWatch tool.

The yield on the U.S. 10-year Treasury bond was up 2.2 basis points at 4.6297%.

The U.S. dollar index, which measures the greenback's strength against a basket of six currencies, held at 101.29, trading around its highest levels of the month. Gold was down 0.1% at $3,997.27.

In Seoul, stocks moved between negative and positive territory on Tuesday as shares in SK Hynix veered between gains and losses, falling as much as 4.7% in the first few minutes of trading before rallying to trade up to 4.6% higher. The volatility for the memory chipmaker comes after a dramatic plunge a day earlier following its Nasdaq debut last week.

In cryptocurrencies, bitcoin was up 0.3% at $62,318.43 while ether moved 0.7% higher to $1,777.63.

(Reporting by Gregor Stuart Hunter; Editing by Muralikumar Anantharaman)