In this paper we investigate the presence and temporal evolution of galactic cosmic rays (GCRs) timeseries and three solar parameters, namely the daily sunspot number, the coronal green line and the 10.7 cm solar radio flux over the period 1996-2003 by the wavelet technique. A number of short-and intermediate-term quasiperiodicities were also detected in both GCR and solar parameters. For the short-term range, we have identified quasiperiods of 16-30 days, 40-55 days, 60-70 days, 80-90 days and 80-100 days. In the case of intermediate range, the significant periods were 120-140 days, 150-170 days, 190-210 days, 240-260 days, ≈1.09 yr. and ≈1.23 yr. The wavelet power spectra show that all the above-mentioned periods are intermittent in nature and occurred in different time-series in different intervals. The result exhibits that the well-known "Rieger period" of (150-160 days) was prominent in both GCR and solar data sets during the ascending phase of cycle 23. Possible reasons behind the observed periods were discussed with the help of previous results and existing numerical models.