A Bush aide later contended the two leaders are in agreement on possible sanctions against Iran.
The two leaders met on the sidelines of the U.N. General Assembly. The meeting lasted 5 minutes longer than scheduled.
Among the issues both countries face are Iran, Syria, the Palestinian-Israeli conflict and Darfur.
"Relations between the United States and France have been long-standing and deeply rooted," Chirac said, adding, "We have discussed today that we have a common approach" on Iran.
"Iranians got to understand we share the same objective," Bush said in response to a question. He added, "We believe time is of the essence."
Both Bush and Chirac said Iran must be convinced to end its uranium enrichment program.
At a press briefing later in the day, Judy Ainsley of the National Security Council maintained that the two presidents had been in agreement on Iran in spite of Chirac's failure to mention sanctions in his speech to the General Assembly.
"President Chirac has historically not liked sanctions, he's very up front about that," she said. "He doesn't think that they're effective. However, he has not taken them off the table, including in the Iran case, if that's the option that ends up being the one that people choose if negotiations don't succeed. What he talked about is trying to see if there was a framework where negotiations could go forward."