(Reuters) - Brent crude prices fell on Tuesday as a lower demand growth estimate and raised supply forecast from the International Energy Agency countered support from a rebound by stock markets and a weaker dollar that lifted U.S. crude.

Brokers and analysts continued to note an unwinding of the Brent-U.S. crude spread trade, with Brent's premium to its U.S. counterpart narrowing.

The Paris-based IEA, advisor to 28 industrialized countries on energy policy , raised its forecast for Libyan crude oil production by the end of 2011. It said OPEC oil output also had risen and cut its estimate for demand growth, citing financial and economic head winds.

Brent crude and the U.S. product markets are weaker, on demand concerns reinforced by an (IEA) monthly report that trimmed demand, Tim Evans, energy analyst at Citi Futures Perspective in New York, said in a note.

Evans said U.S. crude was supported as traders focused on a firmer equity market, a weaker U.S. dollar (or recovering euro), and expectations that U.S. commercial crude stocks may have declined last week.

ICE Brent October crude fell 69 cents to $111.56 a barrel by 11:53 a.m. EDT, slipping after reaching $113.30. The October Brent contract expires on Thursday.

U.S. October crude rose 97 cents to $89.16 a barrel, having stalled at $89.93, ahead of the $90 level.

Brent's premium to U.S. crude was below $23 a barrel, after its surge to a record above $27 last week.

We still view the $22-25 zone as a sweet spot for the nearby Brent-WTI spread, at least until some cargoes of Libyan supply into Europe are realized, Jim Ritterbusch, president at Ritterbusch & Associates, said in a research note.

The dollar index .DXY, measuring the greenback against a basket of other currencies, was down 0.6 percent. The euro fell against the yen after a disappointing Italian debt auction and conflicting reports about fresh euro zone support for debt-laden Greece.

But the euro rose against the dollar, bolstered by initial gains in U.S. stocks and a Reuters report quoting a Greek government official as saying Greek, German, and French leaders would hold a conference call on Wednesday.

Ahead of weekly reports on U.S. oil inventories, a survey of analysts on Monday yielded a forecast for crude stocks to have fallen 3 million barrels last week on disrupted production and imports due to Tropical Storm Lee.

(Additional reporting by Gene Ramos in New York, Jessica Donati in London and Alejandro Barbarosa in Singapore; Editing by David Gregorio)