Large institutional investors continued to pile money into oil, which is giving better returns than investments in stocks and bonds, further heating up prices, they said.
The Commonwealth Bank of Australia said in a market commentary that the "oil price also benefited from further US dollar weakness."
New York's main oil futures contract, light sweet crude for July delivery, briefly rose to a high of $135.04 a barrel before easing to $134.59 in Asian afternoon trade, up $1.42 from its US close.
The benchmark futures contract had closed a whopping $4.10 higher at a record $133.17 on the New York Mercantile Exchange, and continued its upward spiral in after-hours electronic trade.
London's Brent crude contract for July was also busting records, rising to a high of $134.50 before pulling back to trade at $134.36, smashing its intraday peak of 133.34 dollars set a day earlier.
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In unadjusted terms, New York oil has risen more than fourfold compared with five years ago when it was trading at just below 30 dollars a barrel.
"Currently, market psychology is trumping fundamentals," said Victor Shum, an analyst with energy consultancy Purvin and Gertz in Singapore.
"The psychology is that the oil market is tight. Even though there is no shortage, global oil demand continues to grow and supply growth is restrained," he added.