By Gertrude Chavez-Dreyfuss

NEW YORK, July 18 (Reuters) - U.S. Treasury yields fell on Tuesday, as investors grew cautious about the latest political drama in Washington around healthcare legislation and more data pointed to benign inflation with a drop in import prices for a second straight month.

Yields on the 10-year note, which move inversely to prices, dropped to three-week lows, while those on the 30-year bond slid to their lowest in two weeks.

"The uncertainty in Washington may be giving a little bit of a bid in Treasury prices," said Lou Brien, market strategist at DRW Trading in Chicago.

After two Republicans said they would not back the latest Obamacare rollback bill, Senate Republican Leader Mitch McConnell was weighing a vote on simply repealing the 2010 healthcare law with no replacement.

Investors fretted about the growing division within U.S. President Donald Trump's Republican party that has hampered the administration's legislative policy goals.

Tuesday's economic data also weighed on sentiment.

U.S. import prices fell for a second straight month in June amid further declines in the cost of petroleum products, evidence of tepid inflation that could further reduce chances of another Federal Reserve interest rate hike in December.

In mid-morning trading, U.S. 10-year yields fell to 2.267 percent from 2.309 percent late on Monday. Yields earlier hit a three-week low of 2.266 percent.

DRW's Brien said the drop below the key 2.30 percent yield on the 10-year was a significant technical indicator that would suggest further buying in Treasuries.

The next key level for 10-year yields would be 2.25 percent, Brien added.

U.S. 30-year bonds were down 21/32 in price to yield 2.859 percent, from 2.893 percent Monday. Those yields earlier touched a two-week low of 2.858 percent.

U.S. two-year yields were down at 1.351 percent from Monday's 1.36 percent.

The yield curve continued to flatten on Tuesday. The gap between shorter-dated and longer-dated Treasury yields fell further, with the spread between five-year and 30-year yields narrowing to 103.90 basis points.

The same was true for the spread between U.S. two-year and 10-year notes, with the gap shrinking slightly to 92.10 basis points, the tightest in two weeks.

Analysts, however, continued to price in a steepening of the yield curve, as a move away from interest rate hikes would support Treasury prices on the short end, while low inflation would prompt investors to sell the long end of the curve. (Editing by Meredith Mazzilli)