* Oil prices regain some ground after sharper drops earlier Monday
* Demand for three- and 10-year Treasury notes remains strong
* S&P 500 little changed on Monday (Updates with U.S. Treasury auction, changes to oil prices)
NEW YORK, March 12 (Reuters) - Oil prices regained some ground on Monday afternoon but remained down as investors grappled with persisting concerns about rising U.S. output, while demand for U.S. Treasuries stayed strong despite increased supply.
Crude prices rose on Friday after the U.S. economy added the biggest number of jobs in more than 1-1/2 years in February. But U.S. crude fell as much as 2.21 percent on Monday, to $60.67 per barrel, before bouncing back to $61.35, down 1.11 percent.
It just looked like some profit taking," said Jim Ritterbusch, president of energy advisory firm Ritterbusch & Associates.
Brent was last at $64.96, down 0.81 percent on the day.
Energy investors are weighing increased U.S. supply against the likelihood that the Organization of the Petroleum Exporting Countries 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 ... but U.S. production, and North American production levels in general, is going to negate a lot of the impact of that," said Gene McGillian, director of market research at Tradition Energy.
Friday's strong U.S. payroll data, which showed a hefty 313,000 rise in jobs but tempered growth in hourly earnings, supported Treasuries in Monday trade.
Benchmark 10-year notes last rose 8/32 in price to yield 2.8663 percent. That is not far off the 2.957 percent yield on Feb. 21, the highest since the instrument yielded more than 3 percent in January 2014.
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 notes, 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."
Last week's U.S. jobs data, as well as an easing of fears of a global trade war, boosted stocks across many parts of the world.
MSCI's world equity index hit a two-week high, while Hong Kong's Hang Seng Index closed up 1.93 percent.
Emerging market stocks rose 1.29 percent.
U.S. stocks, though, were mixed on Monday, with the S&P 500 down 2.08 points, or 0.07 percent, at 2,784.49 and the Dow Jones Industrial Average lower by 127.52 points, or 0.5 percent, at 25,208.22.
The Nasdaq Composite was up 33.19 points, or 0.44 percent, at 7,594.00.
Wall Street's main indexes closed up nearly 2 percent on Friday on the strength of the jobs report, and have nearly reversed declines in recent weeks when investors feared that higher wages might lead to price pressures.
"We're seeing some positive follow-through, but it would not surprise me to see some profit-taking coming off a very powerful performance on Friday," said Andre Bakhos, managing director at New Vines Capital LLC in Bernardsville, New Jersey.
In currencies, investors' appetite for riskier bets caused the U.S. dollar to inch down. The dollar index fell 0.24 percent, with the euro up 0.26 percent at $1.2337.
The Japanese yen strengthened 0.41 percent versus the greenback to 106.35 per dollar, while sterling was last trading at $1.3908, up 0.42 percent on the day.
(Reporting by Nick Brown; Additional reporting by Kate Duguid and Ayenat Mersie; Editing by Steve Orlofsky Editing by Nick Zieminski)