A solar-pumped laser with bulk active medium generally requires a considerable amount of concentrated solar power for initiating laser emission. In previous work, 54.9 W threshold incoming solar power was found for a Ce:Nd:YAG solar laser by a 0.075 m2 effective area parabolic mirror. In the present work, a 0.0615 m2 area Fresnel lens was used to concentrate incoming solar power to a 2 mm diameter, 30 mm length Ce:Nd:YAG rod. 1.81 W continuous-wave 1064 nm solar laser output power was measured, corresponding to 3.15% solar-to-laser conversion efficiency, 4.4% laser slope efficiency, and 29.4 W/m2 collection efficiency. More importantly, threshold incoming solar power as low as 16.5 W was achieved, representing a 3.33 times reduction in threshold solar power, as compared to previous record by the parabolic mirror. By using a 0.0855 m2 area Fresnel lens, 2.83 W solar laser power was also measured, leading to 3.56% solar-to-laser conversion efficiency, 4.9% laser slope efficiency, and 33.1 W/m2 collection efficiency. Low threshold incoming solar power of 22.7W was also obtained, representing a 2.42 times reduction in threshold solar power in relation to the previous record. Notably, 1.41 W TEM00 mode solar laser power was also measured by adopting an asymmetric laser resonant cavity, resulting in 2.06% solar-to-TEM00 mode laser conversion efficiency, which, to the best of our knowledge, is 2.61 times larger than the previous record by Nd:YAG medium.