Context. Detailed chemical abundances of volatile and refractory elements have been discussed in the context of terrestrial-planet formation during in past years. Aims: The HARPS-GTO high-precision planet-search program has provided an extensive database of stellar spectra, which we have inspected in order to select the best-quality spectra available for late type stars. We study the volatile-to-refractory abundance ratios to investigate their possible relation with the low-mass planetary formation. Methods: We present a fully differential chemical abundance analysis using high-quality HARPS and UVES spectra of 61 late F- and early G-type main-sequence stars, where 29 are planet hosts and 32 are stars without detected planets. Results: As for the previous sample of solar analogs, these stars slightly hotter than the Sun also provide very accurate Galactic chemical abundance trends in the metallicity range -0.3 < [Fe/H] < 0.4. Stars with and without planets show similar mean abundance ratios. Moreover, when removing the Galactic chemical evolution effects, these mean abundance ratios, Δ [X/Fe] SUN - STARS, against condensation temperature, tend to exhibit less steep trends with nearly zero or slightly negative slopes. We have also analyzed a subsample of 26 metal-rich stars, 13 with and 13 without known planets, with spectra at S/N ~ 850, on average, in the narrow metallicity range 0.04 < [Fe/H] < 0.19. We find the similar, although not equal, abundance pattern with negative slopes for both samples of stars with and without planets. Using stars at S/N ≥ 550 provides equally steep abundance trends with negative slopes for stars both with and without planets. We revisit the sample of solar analogs to study the abundance patterns of these stars, in particular, 8 stars hosting super-Earth-like planets. Among these stars having very low-mass planets, only four of them reveal clear increasing abundance trends versus condensation temperature. Conclusions: Finally, we compared these observed slopes with those predicted using a simple model that enables us to compute the mass of rocks that have formed terrestrial planets in each planetary system. We do not find any evidence supporting the conclusion that the volatile-to-refractory abundance ratio is related to the presence of rocky planets. Based on observations collected with the HARPS spectrograph at the 3.6-m telescope (072.C-0488(E)), installed at the La Silla Observatory, ESO (Chile), with the UVES spectrograph at the 8-m Very Large Telescope (VLT) - program IDs: 67.C-0206(A), 074.C-0134(A), 075.D-0453(A) -, installed at the Cerro Paranal Observatory, ESO (Chile), and with the UES spectrograph at the 4.2-m William Herschel Telescope (WHT), installed at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias, on the island of La Palma.Tables A.1-A.8 are only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/552/A6