DALLAS—Just hours before her son George W. Bush formally opens his presidential library here, former first lady Barbara Bush dismissed talk of a presidential run by another son, Jeb, in 2016.

In an interview with NBC’s ‘Today" show, Barbara Bush said she believed Jeb, a former Florida governor, was “the best qualified” to seek the Republican presidential nomination, but that he shouldn’t run.

“We’ve had enough Bushes,” Barbara Bush told NBC, adding there are other “people out there” who are qualified. “It’s a great country. There are a lot of great families and it's not just four families or whatever.”

Her remarks come just a day after George W. Bush told ABC and CNN that he believes his brother should seek the presidency. Former first lady Laura Bush, who joined Barbara Bush in the “Today" show interview, said her brother-in-law would be a “terrific president,” but declined to say whether she thinks he'll run.

“We don’t know, and we’re just letting him decide,” Laura Bush said.