Context. The solar spectrum is a primary reference for the study of physical processes in stars and their variation during activity cycles. High resolution spectra of the Sun are easily obtained from spatially selected regions of the solar disk, while those taken over the integrated disk are more problematic. However, a proxy can be obtained by using solar light reflected by small bodies of the solar system. Aims: In November 2010 an experiment with a prototype of a laser frequency comb (LFC) calibration system was performed with the HARPS spectrograph of the 3.6m ESO telescope at La Silla during which high signal-to-noise spectra of the Moon were obtained. We exploit those Echelle spectra to study a portion of the optical integrated solar spectrum and in particular to determine the solar photospheric line positions. Methods: The DAOSPEC program is used to measure solar line positions through Gaussian fitting in an automatic way. The solar spectra are calibrated both with an LFC and a Th-Ar. Results: We first apply the LFC solar spectrum to characterize the CCDs of the HARPS spectrograph. The comparison of the LFC and Th-Ar calibrated spectra reveals S-type distortions on each order along the whole spectral range with an amplitude of ±40 m s-1 . This confirms the pattern found in the first LFC experiment on a single order and extends the detection of the distortions to the whole analyzed region revealing that the precise shape varies with wavelength. A new data reduction is implemented to deal with CCD pixel inequalities to obtain a wavelength corrected solar spectrum. By using this spectrum we provide a new LFC calibrated solar atlas with 400 line positions in the range of 476-530, and 175 lines in the 534-585 nm range corresponding to the LFC bandwidth. The new LFC atlas is consistent on average with that based on FTS solar spectra, but it improves the accuracy of individual lines by a significant factor reaching a mean value of ≈10 m s-1 . Conclusions: The LFC-based solar line wavelengths are essentially free of major instrumental effects and provide a reference for absolute solar line positions at the date of Nov. 2010, i.e. an epoch of low solar activity. We suggest that future LFC observations could be used to trace small radial velocity changes of the whole solar photospheric spectrum in connection with the solar cycle and for direct comparison with the predicted line positions of 3D radiative hydrodynamical models of the solar photosphere. The LFC calibrated solar atlas can be also used to verify the accuracy of ground or space spectrographs by means of the solar spectrum. Observations based on the ESO 3.6 m telescope at La Silla, Chile.Full Table 3 and a solar spectrum are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/560/A61