The Bush family, which already has produced two U.S. presidents, is in disagreement about whether there should be a third - former Florida Governor Jeb Bush.
Former first lady Barbara Bush, said son Jeb is the most qualified Republican to run in 2016, but told NBC's Today show, "We've had enough Bushes."
Former President George W. Bush takes the other side in the intra-family debate.
"He would be a marvelous candidate if he chooses to do so," he told ABC News. "He doesn't need my counsel because he knows what it is, which is: 'run.' But whether he does or not is a very personal decision."
Barbara Bush, known for her blunt talk, said of her second-born son, "There are other people out there that are very qualified... He's the most qualified but I don't think he'll run."
The conflicting messages come as the 43rd president, who held office from 2001 to 2009, prepared to unveil his presidential library in Dallas, accompanied by all the living U.S. presidents, including his father, George H.W. Bush, who occupied the White House from 1989 through 1992.
The library opening will highlight George W. Bush's two stormy terms, which included the September 11, 2001, attacks, wars in Afghanistan and Iraq, and the 2008 financial crisis.
The event also puts the Bush family back in the spotlight at a time when their Republican Party is re-assessing itself following a loss in the 2012 presidential campaign.
Bush and his father have represented a more traditional side of the Republican Party, which now faces challenges from its more strident Tea Party wing.
Polls have shown Jeb Bush trailing other Republicans, such as Senators Marco Rubio of Florida and Rand Paul of Kentucky, both favorites of the Tea Party movement.
A Public Policy Polling survey earlier this month found 12 percent of potential voters said they would most like to see Jeb Bush as the Republican candidate in 2016, while Rubio topped out with 21 percent, followed by Paul with 17 percent.
John Adams (1979-1801) and John Quincy Adams (1825-1829) are the only other father and son to serve as U.S. president.