To assert or declare firmly — to state something confidently and without hesitation.
彼が犯人だと断言する証拠はまだ揃っていない。
There is not yet sufficient evidence to assert that he is the culprit.
専門家はこの薬の効果を断言したが、追加の研究が必要だ。
The expert affirmed the effectiveness of this medicine, but additional research is needed.
彼女は『これは間違いだ』と断言した。
She declared, 'This is wrong.'