The verb retract means to take back an offer or statement, etc. or admit that a statement was false.

Synonyms are back down, back off, cancel, or deny.

The word origins from Old French (14th century) retracter meaning “to draw (something) back” and directly from Latin retractus, past participle of retrahere meaning “to draw back”. The sense of “to revoke, recant, take back” is attested from the 1540s.

She was forced to retract an opinion about the sensitive topic.

Mr. Ben hurriedly asked to retract the statement, but it had just been broadcast on public radio.

He refused to retract what he said no matter what happens.