(CNN) -- Sen. Barack Obama's grandmother, Madelyn Dunham, has died following a bout with cancer, Obama and his sister, Maya Soetoro-Ng, said Monday.

She was 86.

At a rally in Charlotte, North Carolina, Monday night, the Illinois senator said "she has gone home and she died peacefully in her sleep with my sister at her side."

"I'm not going to talk about it long because it's hard to talk about," he added.

Obama remembered her as "one of those quiet heroes we have across America, who aren't famous ... but each and every day they work hard. They look after their families. They look after their children and their grandchildren."

In a statement released Monday afternoon, Obama and his sister said that Dunham was "the cornerstone of our family, and a woman of extraordinary accomplishment, strength, and humility." Watch CNN contributors discuss Obama's grandmother »

"She was the person who encouraged and allowed us to take chances. She was proud of her grandchildren and great-grandchildren and left this world with the knowledge that her impact on all of us was meaningful and enduring. Our debt to her is beyond measure."

Obama and Soetoro-Ng asked that donations be made for the search for a cure for cancer in lieu of flowers. A small private ceremony will be held "at a later date."

Dunham passed away peacefully at her home shortly before midnight Sunday night (5 a.m. ET), campaign spokeswoman Jen Psaki told CNN. She said Obama learned of her death around 8 a.m.

Obama's republican rival, Sen. John McCain, issued a statement Monday afternoon:

"We offer our 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."

The Democratic presidential candidate left the campaign trail on October 23 and flew to Honolulu, Hawaii, to spend the day with Dunham, whose health deteriorated after she suffered a broken hip.

His wife, Michelle Obama, filled in for him at events in Columbus and Akron, Ohio, on October 24.

Obama said in an interview taped for that day's "Good Morning America" that Dunham had been "inundated" with flowers and messages from strangers who read about her in Obama's 1995 book, "Dreams From My Father."

"Maybe she is getting a sense of long-deserved recognition toward the end of her life," he said. Watch Obama tell supporters that his grandmother was "one of those quiet heroes" »

The candidate resumed his campaign on October 25.

Obama has spoken often about his grandmother -- who helped raise him -- as an integral figure in his youth and how she struggled against the glass ceiling in her career. He and his family traveled to Hawaii in August to visit her.

"She's the one who put off buying a new car or a new dress for herself so that I could have a better life," he said in his acceptance speech at the Democratic National Convention. "She poured everything she had into me. And although she can no longer travel, I know that she's watching tonight, and that tonight is her night as well."

CNN political producer Ed Hornick contributed to this report.

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