For Mr. Obama, Tuesday’s telephone call to Mr. Bush was a political imperative. It is no secret that he opposed the Iraq war, and that as a senator he took a dim view of Mr. Bush’s “surge,” the 2007 troop buildup that many military analysts credit with helping to stabilize Iraq. Leading up to Tuesday night’s address, Republicans were clamoring for Mr. Obama to give the former president credit.

He did not. Instead, he said simply that he had spoken to Mr. Bush earlier in the day, and that while their disagreements were well-known, “no one could doubt President Bush’s support for our troops, or his love of country and commitment to our security.”

The White House declined to discuss the thinking behind that language. But Bush loyalists on Wednesday were more than a little miffed by it.

“I’m curious why he mentioned President Bush at all if he wasn’t going to give him credit for the surge,” said Gordon Johndroe, who was spokesman for Mr. Bush’s National Security Council. A former top Bush speechwriter and strategist, Peter Wehner, said the mention of Mr. Bush “was at best pro forma; at worst, it was patronizing.”