West Texas Intermediate (WTI), the US benchmark, struck a low of $27.92 (S$40.15) a barrel at one point before recovering. It was trading at $28.15, down 31 cents, or 1.09 per cent, at around 0240 GMT.
The last time WTI closed below $28 was in September 2003.
Brent crude -- which briefly fell below $28 on Monday -- was 13 cents lower at $28.63.
"The EIA report played a big part in the price decline," said Phillip Futures analyst Daniel Ang, adding that this underscored the current "bearishness in the market".
He also said the WTI February contract was due to expire later in the week, which could have prompted traders to roll over their positions to the March contract.
The EIA said Tuesday oil prices are set to fall further this year as supply vastly exceeds demand, with major oil exporter Iran's return to the market offsetting any production cuts from other countries.
"Can it go any lower?" the IEA said. "Unless something changes, the oil market could drown in oversupply. So the answer to our question is an emphatic yes. It could go lower."
The market has been awash with supplies owing to high production levels in the United States and in the OPEC cartel, which last year rejected calls to slash output as it looks to maintain its market share.
Prices have crashed about 75 per cent since mid-2014, hit by a perfect storm of a supply glut, weak demand, a slowing global economy and a strong dollar.
The oil crisis has caused ructions across global markets, wiping trillions of dollars off valuations, with weak demand for the commodity signalling weakness in economies. The tumbling prices have also led to major energy firms scaling back or cancelling investment and projects, and laying of thousands of workers.
"Clearly there is a further focus on the potential for Iranian additions to daily supply," said Michael McCarthy, chief market strategist at CMC Markets Australia.
"On top of that, there are further concerns that there's a stockpile to be cleared in Iran now that sanctions have been lifted," he told AFP by telephone from Sydney.
"Coming on top of a very fragile pricing environment, that's clearly had an impact."
Iran on Monday ordered a boost to crude production a day after the West lifted sanctions on the country in response to Tehran's compliance with a deal on curbing its nuclear programme.
Iran's National Iranian Oil Company said it had ordered output to increase by 500,000 barrels per day. The country currently produces 2.8 million barrels per day and exports just over a million.
"It's the supply side that is getting the focus at the moment. The demand aspect is a longer term proposition for the market," added McCarthy.
"We're now outside fundamentals and for that reason it is very difficult to forecast where it will stop. When markets panic, they become unpredictable."