(Updates throughout)
* IEA curbs demand forecast, but also expects less supply
* Tension between Israel and Iran
By Ikuko Kao
LONDON, July 1 (Reuters) - Oil rose more than $2 on Tuesday after the International Energy Agency revived concerns about long-term supply shortages and tension between Israel and Iran raised fears about possible outages in the much nearer term.
U.S. crude <CLc1> rose $2.06 to $142.06 a barrel by 1126 GMT. London Brent crude <LCOc1> rose $2.41 to $142.24.
On Monday, U.S. crude hit an all-time high of $143.67 a barrel in intra-day trade, but later eased, with traders citing evidence high prices were eroding demand, especially in the United States.
On Tuesday, the IEA's medium-term outlook said world oil demand would rise less than previously forecast, but it also said supply would be tighter than anticipated.
"The IEA report today was a little bit bearish on the demand side, but on every other side, it was a little bit bullish," said Christopher Bellew of Bache Financial.
He also cited tension between Israel and OPEC's second biggest oil producer Iran.
Speculation has mounted that Israel plans to attack Iran's nuclear facilities, which Iran says are for purely peaceful purposes, following a big Israeli air force exercise last month.
Iran's Revolutionary Guards said Iran would impose controls on shipping in the Strait of Hormuz if the country were attacked, a newspaper reported at the weekend.
Roughly 40 percent of the world's traded oil moves through the narrow waterway separating Iran from the Arabian Peninsula.
"The market has been worried about the tensions involving Iran and that remains a supportive factor for the oil price," said David Moore, a commodities analyst at the Commonwealth Bank of Australia in Sydney.
Oil prices have risen by more than 40 percent so far this year, eroding fuel demand especially in the Untied States, the world's largest oil consumer.
The U.S. government said on Monday domestic oil demand in April was the lowest for that month since 2002.
The next set of data from the U.S. government, to be released on Wednesday, is expected to show a 200,000-barrel fall in overall crude stocks, according to a Reuters poll of analysts. [
]Distillates, including diesel, were predicted to rise by 1.4 million barrels and gasoline stocks were forecast to edge 100,000 barrels higher.
(Additional reporting by Chua Baizhen and Luke Pachymuthu in Singapore)