* Treasuries prices rise in choppy trading
* Debt reduction plan seen disappointing investors
* US CDS costs fall, risk seen below that of Germany (Recasts, updates prices)
By Karen Brettell
NEW YORK, July 19 (Reuters) - U.S. Treasuries prices gained on Tuesday in choppy trading as investors sought more signs that Washington will agree to cut the deficit and raise the debt ceiling, while fears over contagion from euro zone debt woes maintained a safety bid for U.S. paper.
Prices reversed earlier losses as investors tiptoed back into riskier assets including stocks, and some feared that plans to cut the U.S. deficit will disappoint the market.
"Stocks have given back some of the gains and as stocks have sold off the bonds have caught a little bit of a bid," said James Newman, head of Treasury and Agency trading at Keefe, Bruyette and Woods in New York.
Bonds were also boosted by continued uncertainty over how Europe will resolve Greece's debt woes, ahead of a key meeting of European leaders on Thursday.
"There's a lot of uncertainty in the market still; I think people want to see the debt ceiling thing resolved and the European situation is still unresolved as well," Newman added.
Most Treasuries prices declined earlier, though long bonds recovered from a dramatic sell-off on Monday and outperformed on Tuesday.
The gap between two-year and 10-year notes, by contrast, widened, in an indication that concerns over the deficit reduction and continuing disagreement over raising the debt ceiling are continuing to weigh on government debt.
Lawmakers in Washington are seeking spending cuts before agreeing to raise the debt ceiling, with only four days remaining before President Obama's deadline to reach a deal.
As the deadline nears, a "Plan B" introduced last week by Senate Republican leader Mitch McConnell, which will include fewer cuts than some had hoped for, is seen as the most likely agreement to end the debt standoff.
"I think that at the end of the day (it) will leave the market somewhat underwhelmed," said Carl Lantz, interest rate strategist at Credit Suisse in New York.
"You'll have to deal with the fallout from raising people's expectations and then under-delivering, which I think for Treasuries means a bit higher yields and a bit steeper curve," he said.
The plan could also pave the way for a rating downgrade from Standard & Poor's, which last week said it may cut the country's rating from the top AAA if there is no progress in reducing the country's deficit, regardless of any agreement on raising the debt ceiling.
The cost of insuring U.S. debt in the credit default swap market fell, after moving back to its recent highs, though the contracts continued to reflect a very low perceived probability of a default.
Five-year protection costs, the most liquid contract, fell by 2 basis points to 54 basis points, or $54,000 per year for $10 million in debt, according to Markit.
Germany's CDS also fell, though it remained above U.S. protection costs, suggesting that investors see contagion from the euro zone as a larger concern than the potential problems posed by the U.S. debt ceiling debate.
German CDS fell 2 basis points to 62 basis points, Markit data show.
Treasuries also temporarily extended losses after data showed that U.S. housing starts rose more than expected in June to touch a six-month high. For more see [ID:nCAT005473].
"Despite this out-sized monthly gain, it really does not suggest a return to (a) strong housing market," said Lindsey Piegza, economist at FTN Financial in New York. "We are still very much bouncing along the bottom."
Benchmark 10-year notes US10YT=RR were last up 4/32 in price to yield 2.92 percent, little changed from Monday.
Five-year notes US5YT=RR rose 1/32 in price to yield 1.44 percent, up from 1.43 percent, and 30-year bonds US30YT=RR rose 16/32 in price to yield 4.28 percent, down from 4.31 percent on Monday. (Additional reporting by Alex Alper; Editing by James Dalgleish)