The US currency rose against the euro after the failure of Greek coalition parties to approve terms of a new bailout package fanned fears that a disorderly default could spread to other debt-ridden, euro zone countries.
Many commodities that trade in dollars -- including gold, copper and cocoa -- fell as the greenback's rise made it costlier for investors using other currencies to buy positions in those markets.
The 19-commodity Thomson Reuters-Jefferies CRB index settled flat, however, after markets such as wheat, coffee and sugar rose to offset losses elsewhere in the complex.
US crude oil, which accounts for roughly a quarter of the CRB's weighting, closed down 1 percent at $96.91 per barrel. It fell in response to the stronger dollar and continued concerns about weak consumption and rising stockpiles amid unseasonably warm winter weather in the United States.
In Europe, however, frigid temperatures pushed up London's Brent crude for a fifth straight session as investors bet on higher demand for heating material.
European gasoil led gains across the energy complex, rising more than 3.5 percent as bitter weather killed another 33 people in Europe.
Italy said it would allow electricity providers to fire up oil-fueled generators to limit the impact of lower natural gas imports after six straight days of reduced supplies from Russia.
Additional support for Brent came as a result of concerns over supplies from OPEC members Iran and Nigeria.
"The cold weather is giving us a lift in the products and that is feeding through to Brent," said Rob Montefusco, a trader at Sucden Financial in London. "Also, any sort of trouble in the Middle East is likely to keep Brent well bid."
Brent's front-month contract settled up 1.2 percent at $115.93 a barrel, its highest close since Aug. 2.
That brought the discount for US crude versus Brent to more than $19 per barrel -- a level last seen in early November.
Copper began a new trading week on shaky ground, falling under the weight of the dollar and European debt-contagion fears. The metal's benchmark three-month futures contract in London closed down $75 at $8,500 a tonne -- 2 percent below a January peak of $8,679.50.
Gold edged lower, extending Friday's 2 percent drop that came after encouraging US payrolls data smashed hopes of extra stimulus from the Federal Reserve. Expectations of new Fed action had helped gold climb 11 percent in January.
Spot gold, which tracks trades in bullion, was down 0.3 percent at $1,720.86 by late Monday afternoon in New York.
Wheat futures in Chicago closed up 1.2 percent at $6.68-1/2 per bushel, snapping a two-session losing streak.
Chicago-traded soybeans ended flat at around $12.33 a bushel, after initially rising to a three-month high, as frozen wheat fields in Europe and dryness in soy-growing parts of South America threatened that crop.