Nanoparticles of superconducting YBa₂Cu₃O_7−δ were synthesized via a citrate pyrolysis technique. Room temperature ferromagnetism was revealed in the samples by a vibrating sample magnetometer. Electron spin resonance spectra at selected temperatures indicated that there is a transition from the normal to the superconducting state at temperatures below 100 K. The M–T curves with various applied magnetic fields showed that the superconducting transition temperatures are 92 K and 55 K for the air-annealed and the post-annealed samples, respectively. Compared to the air-annealed sample, the saturation magnetization of the sample by reheating the air-annealed one in argon atmosphere is enhanced but its superconductivity is weakened, which implies that the ferromagnetism maybe originates from the surface oxygen defects. By superconducting quantum interference device measurements, we further confirmed the ferromagnetic behavior at high temperatures and interesting upturns in field cooling magnetization curves within the superconducting region are found. We attributed the upturn phenomena to the coexistence of ferromagnetism and superconductivity at low temperatures. Room temperature ferromagnetism of superconducting YBa₂Cu₃O_7−δ nanoparticles has been observed in some previous related studies, but the issue of the coexistence of ferromagnetism and superconductivity within the superconducting region is still unclear. In the present work, it will be addressed in detail. The cooperation phenomena found in the spin-singlet superconductors will help us to understand the nature of superconductivity and ferromagnetism in more depth.