A measurement by microlensing of the planetary mass function of planets with masses ranging from 5M_E to 10M_J and orbital radii from 0.5 to 10 AU was reported recently. A strategy for extending the mass range down to (1-3)M_E is proposed here. This entails monitoring the peaks of a few tens of microlensing events with moderately high magnifications with 1-2m class telescopes. Planets of a few Earth masses are found to produce deviations of ~ 5% to the peaks of microlensing light curves with durations ~ (0.7-3)hr in events with magnification ~ 100 if the projected separation of the planet lies in the annular region (0.85-1.2)r_E. Similar deviations are produced by Earth mass planets in the annular region (0.95-1.05)r_E. It is possible that sub-Earths could be detected very close to the Einstein ring if they are sufficiently abundant, and also planetary systems with more than one low mass planet. ; Comment: 12 pages, 20 figures (in press) MNRAS (2013)