US crude was 7 cents up at $95.01 a barrel by 1633 GMT. ICE Brent crude was 17 cents lower at $111.60 a barrel.
Oil prices have been supported by gains in global equity markets since last week, Christopher Bellew, oil trader with Jefferies Bache, said. "I think the stock market rebound indicates some confidence in growth," he said.
The MSCI world equity index rose 0.1 percent to hit its highest since June 1.
European shares rose for a sixth straight session on Monday on expectations that US economic recovery remained on track, although banks fell on Standard & Poor's negative view over the private sector involvement in a second Greek bailout package.
The euro slipped from one month high against the dollar.
The oil market would have been more volatile if US markets had not shut on Monday, some analysts said.
"With US markets closed for the Independence Day, we are not likely to see much direction in prices today and trade near the previous day's close," Harry Tchilinguirian, BNP Paribas' head of commodity markets strategy, said.
US GASOLINE DEMAND
Analysts also pointed out that oil's fundamentals remained relatively weak.
The Independence Day holiday is traditionally seen by oil traders as marking the height of US gasoline demand. However, US travel group AAA said in late June road travel at the weekend would fall 2.5 percent from a year ago as expensive gasoline eats at driving demand.
"US refiners will be praying that plenty of drivers hit the road over the holiday weekend to give a boost to weary gasoline demand fundamentals. However, projections are not very hopeful," JBC Energy said in its research note.
The International Energy Agency's (IEA) emergency stock release continued to be a focus for oil markets.
The tender to sell crude oil from US strategic petroleum reserves (SPR) as a part of the IEA stock release was oversubscribed by active bids.
But analysts pointed out a lack of coordination and transparency outside the United States and that the full volume of 60 million barrels may not be absorbed due to globally weak demand.
The IEA told a news briefing on Monday that it hoped a very sizeable portion of its oil stock release will be taken up by the market.
ICE DATA
Speculators betting on oil cut net-long positions in the week to June 28 in a continuation of the previous week's trend, data from the IntercontinentalExchange (ICE) showed on Monday.
Data from the US Commodity Futures Trading Commission (CFTC) on Friday also showed hedge funds and other large speculators cut their net long US crude futures and options positions in New York and London last week to the lowest level since November as prices slid.
US oil inventory data from industry group the American Petroleum Institute and the government's Department of Energy will be delayed by a day to Wednesday and Thursday, respectively, due to the Independence Day holiday.
In Libya, whose crude export disruption led to the IEA stock release, the government has had meetings in foreign capitals with representatives of the opposition to try to negotiate a peace deal, a spokesman for Muammar Gaddafi's administration said on Monday.
In the North Sea, oil output at the UK's largest oilfield, the Buzzard field, resumed at the weekend after a brief stoppage last week, trading sources said on Monday.
Copyright Reuters, 2011