NEW YORK, Sept 13 (Reuters) - U.S. Treasury yields rose and the inversion of a closely watched part of the yield curve increased on Tuesday after monthly U.S consumer prices rose again in August instead of declining as bond and equity markets had widely expected. The gap between yields on two- and 10-year notes US2US10=RR, seen as a recession harbinger, was at -27.3 basis points. The consumer price index gained 0.1% last month after being unchanged in July, the Labor Department said on Tuesday.