We report and analyze here observations of strong infrared emissions from the limb of the Venus upper atmosphere during daytime, taken by the Visible and Infrared Thermal Imaging Spectrometer (VIRTIS) aboard Venus Express. We focus on the measurements taken during the first 4 months of nominal operations. The emissions observed at 4.3 mum and at 2.7 mum are attributed to CO₂ fluorescence of solar radiation and are detected up to about 160 km and 130 km, respectively, while the CO fluorescence at 4.7 mum is observed up to about 120 km. The emissions are detected in both the channels of VIRTIS, at different spatial and spectral resolutions (resolving powers about 1800 and 400), for the periapsis and the apoapsis of the Venus Express orbit. From these data sets we built up 2-D maps of the emissions as well as vertical profiles, which are then studied in order to characterize their variations with geophysical parameters, like solar illumination and emission altitude. Several analyses are performed in order to understand the VIRTIS behavior, to determine systematic effects in the data, and to propose appropriate corrections. We also present comparisons with a theoretical nonlocal thermodynamic equilibrium (non-LTE) model of the Venus upper atmosphere. The agreement is very encouraging, in general, and the main variability observed in the data, with solar zenith angle and altitude, can be understood with the model. We conclude that the present data set opens brilliant perspectives for deriving densities and rotational temperatures in the upper mesosphere and lower thermosphere of Venus.