* Oil closes lower but off session lows
* Demand for three- and 10-year Treasury notes remains strong
* U.S. stocks close mixed on Monday (New throughout, updates prices and market activity to include late afternoon trade and close of U.S. stock markets)
By Nick Brown
NEW YORK, March 12 (Reuters) - Investor concerns about rising U.S. oil output sent crude prices down on Monday, but investors stayed bullish on U.S. Treasuries despite an increased supply of three- and 10-year notes.
U.S. Stocks closed mixed, with the S&P 500 and Dow Jones Industrial Average ending in the red, while the Nasdaq Composite added about 28 points.
Energy investors weighed increased U.S. supply against the likelihood that the Organization of the Petroleum Exporting Countries (OPEC) will maintain supply cuts that have been in effect more than a year.
"The market continues to flip back and forth on the idea that increased global demand and a production cut is going to support prices," said Gene McGillian, director of market research at Tradition Energy.
U.S. crude was last at $61.37, down 1.08 percent. Brent was last at $64.96, down 0.81 percent on the day. During the session, U.S. crude fell as much as 2.21 percent. Some of that early slide was probably profit-taking after a rise on Friday, said Jim Ritterbusch, president of energy advisory firm Ritterbusch & Associates.
On Friday, crude prices rose after U.S. data showed the economy in February added the most jobs in more than 1-1/2 years. The payroll data also supported Treasuries.
On Monday, benchmark 10-year notes last rose 8/32 in price to yield 2.8663 percent, hovering near multi-year highs.
The Treasury on Monday sold $28 billion of three-year notes and $21 billion of the 10-year notes, in what analyst George Goncalves called an "on-the-screws type auction."
Increased supply did not quell demand for the U.S. government debt, a positive sign for the heavy issuance expected in the year ahead.
"Nothing really stood out," said Goncalves, head of U.S. rates strategy at Nomura Securities International in New York. "You can consider that a good thing, given this year will see more and more Treasuries issued."
U.S. stocks closed mixed. The Dow Jones Industrial Average fell 157.13 points, or 0.62 percent, to 25,178.61, the S&P 500 lost 3.55 points, or 0.13 percent, to 2,783.02 and the Nasdaq Composite added 27.52 points, or 0.36 percent, to 7,588.33.
Anwiti Bahuguna, a senior portfolio manager at Columbia Threadneedle in Boston, pointed to after-effects of Friday's employment report.
"We've seen stable, modest wage growth, nothing that should be considered harmful for equity markets," Bahuguna said. "It was a Goldilocks sort of report, and the market is still digesting it. What we're looking ahead to is the inflation report."
The broader trend remained positive for Wall Street's main indexes, which had closed up nearly 2 percent on Friday on the strength of the jobs report. They have nearly reversed declines in recent weeks as investors had begun to fear higher wages might lead to price pressures.
Last week's jobs data, as well as an easing of fears of a global trade war, also boosted stocks across many parts of the world.
MSCI's world equity index hit a two-week high on Monday, while Hong Kong's Hang Seng Index closed up 1.93 percent.
Emerging market stocks rose 1.24 percent.
In currencies, investors' appetite for riskier bets hurt the U.S. dollar. The dollar index fell 0.21 percent, with the euro up 0.27 percent to $1.2338.
The Japanese yen strengthened 0.37 percent versus the greenback to 106.39 per dollar, while sterling was last trading at $1.3906, up 0.40 percent on the day.
Additional reporting by Kate Duguid, April Joyner and Ayenat Mersie; Editing by Steve Orlofsky, Nick Zieminski and David Gregorio