An olive branch is a universal symbol of peace. This means to offer a truce or propose a treaty of peace. The earliest mention of greenery from an olive tree is in the Bible, in Genesis 8:11, when the dove brought back an “olive leaf,” possibly a twig containing leaves, to Noah after the waters of the great deluge subsided, which, like the rainbow, served as an emblem that the disaster was over and men could once again live at peace on earth.
Where did that phrase come from - Extend an olive branch