Intercontinental dual-frequency radio interferometric measurements were carried out during 1978 to 1985 between NASA's Deep Space Network stations in California, Spain, and Australia. Analysis of 6800 pairs of delay and delay rate observations made during 51 sessions produced a catalog of positions of 106 extragalactic radio sources, fairly uniformly distributed over the celestial sphere between −45° and +85° declination. Almost all of the resulting source positions have formal uncertainties between 0.5 and 3 milliarcseconds, with their distributions peaking somewhat below 1 mas. Root-mean-square uncertainties are 2.1 and 2.0 mas for RA and declination, respectively. Evidence is found for a long-term drift of the Earth's rotation axis in inertial space, relative to the 1984 IAU precession and nutation models. Tests for time variability of positions of 32 frequently observed sources place limits at the 1 mas/yr level. Comparisons with independently determined source catalogs of comparable quality show differences of positions of common sources that amount to a few mas, and may indicate the level of systematic errors in VLBI source position measurements.