Updated with new prices and ConocoPhillips upgrade news.

NEW YORK (

TheStreet

) -- Oil futures dipped Tuesday ahead of a barrage of data reports set to come out this week.

On Monday, the November delivery contract gained 82 cents to settle at $66.84 per barrel. But on Tuesday morning, the front-month contract for benchmark crude lost 53 cents to $66.31 on the New York Mercantile Exchange.

Concerns about fundamentals, which among other things appeared to weigh on crude prices late last week, will again be in focus on Tuesday and Wednesday.

Tuesday afternoon, the American Petroleum Institute, an industry trade organization, will release its oil and product inventory data for last week. Wednesday morning, the Energy Department will follow up with its own figures. Expectations are that crude inventories will continue to build this week on top of already high levels.

While oil watchers will keep one eye on events in Iran along with dollar fluctuations, they'll also be looking at a batch of macro trends, including consumer confidence, home sales, manufacturing metrics and other reports to be issued this week. The most widely anticipated will be the Labor Department's monthly unemployment figure, set for Friday.

Among oil equities, shares of

Exxon Mobil

(XOM) - Get Report

fell 24 cents to $69.35 just after the opening bell on Tuesday.

Chevron

(CVX) - Get Report

, too, was tracking lower, down 17 cents at $71.53.

Meanwhile,

ConocoPhillips

(COP) - Get Report

was gaining after the opening bell, adding 27 cents to $45.96. An analyst at Collins Stewart upgraded the stock to buy from hold earlier this morning.

-- Written by Sung Moss in New York

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