TREASURIES-Prices gain on weak stocks, after consumer price decline

* Weak stock markets boosts bond buying

* End of Treasury supply removes weight from market

* Consumer prices fell in December

NEW YORK, Jan 11 (Reuters) - U.S. Treasury prices gained on Friday as stocks opened weaker and after data showed a decline in consumer prices during December, while bonds were also helped the market. Stocks opened lower on Friday after rallying for the past five sessions on hopes of a resolution in the U.S.-China trade dispute and assurances from the Federal Reserve that it would be patient on interest rate hikes. Stocks are a little weaker. They really have dictated the direction of Treasury trading for a while now, said Thomas Simons, a money market economist at Jefferies in New York. The Labor Department also said on Friday its Consumer Price Index dipped 0.1 percent last month amid a plunge in gasoline, though underlying inflation pressures remained firm as rental housing and healthcare costs rose steadily. Bonds were further aided by the completion of $78 billion this week in new coupon-bearing Treasury supply, which has weighed on longer-dated bonds.

Benchmark 10-year notes gained 9/32 in price to

yield 2.699 percent, down from 2.731 percent late Thursday. Yields have risen from one-year lows reached a week ago on improving risk appetite since Federal Reserve Chairman Jerome Powell said on Friday that he was aware of the risks of an economic slowdown and that the U.S. central bank will be patient and flexible in policy decisions this year. Powell on Thursday stressed again that the U.S. central bank can be patient in approving any further rate increases, saying that "especially with inflation low and under control, we have the ability to be patient and watch patiently and carefully. The yield curve also steepened after minutes from the Feds December meeting, released on Wednesday, showed that a range of policymakers said they could be patient about future interest rate increases and a few did not support the central bank's rate increase that month. Trade talks between the United States and China and the ongoing partial U.S. government shutdown remain headwinds for markets. A trade deal with China could be significant, if reached. If we get some indication of progress on that front that could really open things up, it could have a pretty dramatic impact on the inflation environment and change expectations for the Fed too, Simons said.

(Editing by Susan Thomas)

)