In a way that is intended to produce peace or bring about agreement; in a pacifying manner.
Conciliatory + -ily, the adverbial form of the more common adjective conciliatory. The extra suffix layer allows precise modification of verbs and adjectives.
This word is rare because 'conciliatingly' or 'reconcilingly' usually work better, but linguistically it's perfect: 'He conciliatorily offered his hand across the divide.' It carries an extra formal weight that feels diplomatic.
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