Chirac called Mr. Bush and told him in a 20-minute telephone conversation that France is willing to adopt a "pragmatic approach" on postwar issues, said the French leader's spokeswoman, Catherine Colonna.
Among the issues cited by Chirac were Iraq's administration and reconstruction, its rich oil resources, international sanctions still in place against Iraq, and plans for an interim government, Colonna said.
CBS News White House Correspondent Mark Knoller reports that when asked if the call had been positive, White House spokesman Ari Fleischer replied, "From the president's point of view, I would call it a businesslike conversation."
The president "made the point that a new liberated Iraq will be much better off than it would have been otherwise," said an unnamed White House official.
"They talked about Syria and they both agreed that Syria should not harbor officials from Saddam Hussein's regime," the official said, adding that the two leaders also briefly discussed the upcoming G-8 summit, which France is hosting.
It was the second clear signal in recent days from the French leader that he wants to repair damage done to relations with Washington by their conflicting views of the Iraq war. France led European opposition to the U.S.-led military campaign, sparking anger and boycotts of French products in the United States.
Chirac, according to his spokeswoman, told Bush that his view on the need for the war remains unchanged.
But he appeared to soften his view of the postwar situation. Notably absent from Colonna's account of the phone call were earlier demands from Chirac that the United Nations get a "central role" in post-Saddam Hussein Iraq.
Instead, she said that the United Nations should be involved "as soon as possible." She did not use the word "central."
"France believes that the international community should give itself the best possible chance and thus make room for the United Nations as soon as possible," said Colonna. "It's in the interests of everyone."
She described the two leaders' conversation as "positive." Chirac's office said it was the first time the two men had spoken since Feb. 7, before relations soured when France said it would veto a U.S.-backed resolution at the U.N. Security Council authorizing the use of force against Iraq.
Chirac first signaled Saturday that he hopes to mend ties with Washington, saying: "We can rebuild our unity around the values that all great democracies share."