We present improved and highly accurate International Celestial Reference System (ICRS) equatorial positions for 1,268,732 stars in 16 astrometric calibration regions located around the celestial equator. Each region is about 7.6{deg}x3.2{deg} in area (~24.3 deg^2^), contains a large number of stars (18,767 to 263,810), has stellar densities ranging from 765 to 10,772 stars deg^-2^, covers a wide range in magnitude (9.5<R<17.8, or equivalently 10.0<V<18.3), and is complete to magnitude R~17.2 (V~17.7). All of the observations were taken in 1994-1998 (mean epoch J1996.0) with the Flagstaff Astrometric Scanning Transit Telescope. Furthermore, each region was observed many times with overlapped CCD strip scans, and these data were reduced to star positions using differential reductions. The reference-star positions were taken from the ACT catalog of accurate star positions and proper motions. The star positions presented herein are typically accurate to +/-26mas (+/-12mas precision) in both right ascension and declination, except for the faintest stars, whose errors are about 2 times larger. Similarly, magnitudes were determined for the astrometric calibration stars using standard photometric reductions, and accuracies of +/-18mmag (+/-10mmag precisions) were achieved (about +/-46mmag for the faintest stars)