Obama has described his grandmother as a role model
The grandmother of US candidate Barack Obama has died on the eve of the presidential election.
Madelyn Dunham, 86, had cancer. She had been a key figure in Mr Obama's early life, and helped raise him.
When her health deteriorated last month, the Democratic candidate left the campaign trail for two days to visit her in Hawaii.
Mr Obama has spoken of their strong bond and referred to her in some of his most powerful campaign speeches.
Announcing her death on Monday, Mr Obama said: "She was the cornerstone of our family, and a woman of extraordinary accomplishment, strength, and humility.
"She was the person who encouraged and allowed us to take chances."
His Republican rival, John McCain, and his wife Cindy offered their "deepest condolences to Barack Obama and his family as they grieve the loss of their beloved grandmother".
"Our thoughts and prayers go out to them as they remember and celebrate the life of someone who had such a profound impact in their lives," they said in a statement.
Ten days ago, Mr Obama broke away from the campaign trail to pay one last visit to Ms Dunham, whom he had mentioned at several key moments during his run for the White House.
At his speech to the Democratic Convention, he praised her as a role model - someone who had risen from bank clerk to bank vice-president through endeavour, but who had been prevented from getting to the very top because of her gender.
And in the speech he gave on race in Philadelphia, he spoke of her in connection with his former pastor, Jeremiah Wright - whose inflammatory comments about white America had threatened to derail Barack Obama's presidential campaign.
Although he later cut his ties to the Reverend Wright, at the time he said he could no more disown him than he could disown his white grandmother, who had once admitted her fear of passing black men in the street.