Using a sample of 448.1×106 ψ(3686) events collected with the BESIII detector in 2009 and 2012, we study the decays χc0,2→η′η′ and ηη′. The decays χc2→η′η′, χc0→ηη′ and χc2→ηη′ are observed for the first time with statistical significances of 9.6σ, 13.4σ and 7.5σ, respectively. The branching fractions are determined to be B(χc0→η′η′)=(2.19±0.03±0.14)×10-3, B(χc2→η′η′)=(4.76±0.56±0.38)×10-5, B(χc0→ηη′)=(8.92±0.84±0.65)×10-5 and B(χc2→ηη′)=(2.27±0.43±0.25)×10-5, where the first uncertainties are statistical and the second are systematic. The precision for the measurement of B(χc0→η′η′) is significantly improved compared to previous measurements. Based on the measured branching fractions, the role played by the doubly and singly Okubo-Zweig-Iizuka disconnected transition amplitudes for χc0,2 decays into pseudoscalar meson pairs can be clarified.