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President Obama offered to personally give Vice President Joseph R. Biden Jr. money to help out when the vice president’s son became sick, Mr. Biden recalled in an interview that aired on Monday.

Mr. Biden said that when his elder son, Beau, first fell ill while attorney general of Delaware, the vice president worried how his son’s family would get by without his income if he had to step down. Mr. Biden mentioned his concern during one of his weekly private lunches with Mr. Obama.

“I said, ‘But Jill and I will sell the house. We’ll be in good shape,’” Mr. Biden told CNN’s Gloria Borger, referring to his wife, Jill Biden.

“He got up, and he said: ‘Don’t sell that house. Promise me you won’t sell the house,’” Mr. Biden remembered. “He said: ‘I’ll give you the money. Whatever you need, I’ll give you the money. Don’t, Joe. Promise me. Promise me.’ I said, ‘I don’t think we’re going to have to anyway.’ He said, ‘Promise me.’”

Mr. Biden did not have to sell the house. He did not say whether Mr. Obama had ended up giving him money, but left the impression that it had not been necessary.

Mr. Biden recounted the story to show how much Mr. Obama cared for his vice president’s family. Beau Biden, 46, died of brain cancer in May.

