To extend an olive branch is to make an offer of peace or to approach a foe in the spirit of conciliation. The idiom is Biblical in origin, deriving from the story of Noah, where a dove delivers Noah an olive branch as a sign that the floods are receding. But while this is the source of modern usage of the term, olive branches were symbolic of peace (as well as victory) in pre-Biblical Greece and Rome. The ancient origins of the symbolism are unknown.
Examples
Mattel issued its statement late Wednesday, but Greenpeace rejected the company’s olive branch. [Los Angeles Times]
And if he intended to extend an olive branch to his opponents, this is not the message they understood. [Independent]
Hone Harawira has offered an unexpected olive branch to the Maori Party, saying his new Mana movement is prepared to work with his former party for the betterment of Maoridom. [Sunday Star Times]
He extended an olive branch to the powerful Hashed tribal federation and called for a ceasefire. [National Post]