The infinitive form of mesiteuō (G3224). The act of mediating, of guaranteeing a covenant or agreement by standing between parties.
God's act of mediating His own promise through an oath (Hebrews 6:17) reveals something profound about His character. He did not have to add an oath to His already-trustworthy word, but He did so to provide maximum assurance to human hearts that struggle with doubt. The God who cannot lie condescended to swear, accommodating human frailty with divine patience.