To extend an offer or gesture of peace, reconciliation, truce, etc. (to someone), so as to end a disagreement or dispute. (Can also be formulated as "offer someone an olive branch.") The conservatives in Congress seem to be offering an olive branch to Democrats on the issue of raising the debt ceiling. If you find yourself in a spat with a friend, try to be the bigger person and be the one to offer an olive branch. I was still hurt by the way my parents had lied to me, but I decided to offer them an olive branch at Christmas.