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But he added, “There is a community here with very few members that transcends political and policy differences. There is so much shared experience between [presidents] that there is much to talk about that they hold in common. So there’s not a lot of need to talk about where they differ.”

After Mr. Bush left office in 2009, he pledged, “I’m not going to criticize my successor.” And he largely has held to that promise, staying out of the spotlight for the most part in the past four years.

Mr. Bush did criticize Mr. Obama indirectly last month for promoting a tax increase on income of more than $1 million, known as the “Buffett rule,” saying it would hurt small businesses.

“If you raise taxes on the so-called rich, you’re really raising taxes on the job creators,” Mr. Bush said.

And the former president this month endorsed Mr. Romney, although the announcement was about as low-key as possible. He told an interviewer, “I’m for Mitt Romney,” just as the doors to his elevator closed as he was preparing to give a speech in Washington.

While Mr. Bush has been restrained in his public remarks about Mr. Obama, his old running mate has shown no such reticence. Former Vice President Dick Cheney has called the Obama administration “an unmitigated disaster.”

As Mr. Bush prepares to watch his portrait unveiled for posterity, the nation’s 43rd president is undoubtedly aware of how it feels to be in Mr. Obama’s shoes. In June 2004, Mr. Bush played host at the White House for the unveiling of portraits of former President Bill Clinton and former first lady Hillary Rodham Clinton. The event came four years after Mr. Bush had campaigned on the promise to restore “honor and dignity” to the Oval Office — a reference to the Monica Lewinsky scandal that resulted in Mr. Clinton’s impeachment.

At the Clintons’ portrait ceremony, Mr. Bush praised Mr. Clinton’s “incredible energy and great personal appeal.”

“The years have done a lot to clarify the strengths of this man,” Mr. Bush said at the time.

Mr. Carney noted that Mr. Bush and Mr. Clinton nowadays enjoy “a good relationship.”

And in 1995, Mr. Clinton found himself in the same role as he presided over the portrait hanging for Mr. Bush’s father, former President George H.W. Bush, the man whom Mr. Clinton defeated in 1992.

On that occasion, Mr. Clinton said the portrait would stand as a reminder of George H.W. Bush’s “basic integrity and decency and of his entire adult lifetime devoted to public service.”

The elder Mr. Bush and his wife, former first lady Barbara Bush, also will attend the event on Thursday at the White House.

Researcher John Sopko contributed to this article.