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We give a recursive formula for purely real Welschinger invariants of realDel Pezzo surfaces of degree $K^2\ge 3$, where in the case of surfaces ofdegree $3$ with two real components we introduce a certain modification ofWelschinger invariants and enumerate exclusively the curves traced on thenon-orientable component. As an application, we prove the positivity of theinvariants under consideration and their logarithmic asymptotic equivalence, aswell as congruence modulo $4$, to genus zero Gromov-Witten invariants.

Welschinger invariants of real Del Pezzo surfaces of degree $\ge 3$