The magnetic and electronic properties of Sr1-xLaxRuO3 were studied by means of dc-magnetization, ac-susceptibility, specific heat, and electrical resistivity measurements. The dc-magnetization and ac-susceptibility measurements have revealed that the transition temperature and the ordered moment of the ferromagnetic order are strongly suppressed as La is substituted for Sr. The ac-susceptibility exhibits a peak at T* due to the occurrence of spontaneous spin polarization. Furthermore, we observed that T* shows clear frequency variations for x>= 0.3. The magnitude of the frequency shifts of T* is comparable to that of cluster-glass systems, and the frequency dependence is well described in terms of the Vogel-Fulcher law. On the other hand, it is found that the linear specific heat coefficient gamma enhances with the suppression of the ferromagnetic order. The relatively large gamma values reflect the presence of the Ru 4d state at Fermi level, and hence, the magnetism of this system is considered to be tightly coupled with the itinerant characteristics of the Ru 4d electrons. The present experimental results and analyses suggest that the intrinsic coexistence of the spatially inhomogeneous magnetic state and the itinerant nature of the Ru 4d electrons is realized in this system, and such a feature may be commonly involved in La- and Ca-doped SrRuO3.