Watermelon is cultivated worldwide and is mainly grafted onto interspecific squash rootstocks. Light-emitting diodes (LEDs) can be implemented as light sources during indoor production of both species and their spectral quality is of great importance. The objective of the present study was to determine the optimal emission of LEDs with wide wavelength for the production of watermelon and interspecific squash seedlings in a growth chamber. Conditions were set at 22/20 °C temperature (day/night), 16 h photoperiod, and 85 ± 5 μmol m−2 s−1 photosynthetic photon flux density. Illumination was provided by fluorescent (FL, T0) lamps or four LEDs (T1, T2, T3, and T4) emitting varying wide spectra. Watermelon seedlings had greater shoot length, stem diameter, cotyledon area, shoot dry weight-to-length (DW/L) ratio, and Dickson’s quality index (DQI) under T1 and T3, while leaf area and shoot dry weight (DW) had higher values under T1. Interspecific squash seedlings had greater stem diameter, and shoot and root DW under T1 and T3, while leaf and cotyledon areas were favored under T1. In both species, T0 showed inferior development. It could be concluded that a light source with high red emission, relatively low blue emission, and a red:far-red ratio of about 3 units seems ideal for the production of high-quality watermelon (scion) and interspecific squash (rootstock) seedlings.