Citing unidentified American officials, the newspaper said more than 100 Israeli F-16 and F-15 fighters took part in the maneuvers over the eastern Mediterranean and Greece in the first week of June.
It said the exercise appeared to be an effort to focus on long-range strikes and illustrates the seriousness with which Israel views Iran's nuclear program.
The newspaper said Israeli officials would not discuss the exercise.
A spokesman for the Israeli military would say only that the country's air force "regularly trains for various missions in order to confront and meet the challenges posed by the threats facing Israel," according to the Times.
A Pentagon official who the Times said was briefed on the exercise, said one goal was to practice flight tactics, aerial refueling and other details of a possible strike against Iran's nuclear installations and long-range conventional missiles.
The official, who spoke on condition of anonymity, said a second goal was to send a clear message that Israel was prepared to act militarily if other efforts to stop Iran from producing bomb-grade uranium fail.
"They wanted us to know, they wanted the Europeans to know, and they wanted the Iranians to know," the Pentagon official said, according to the Times. "There's a lot of signaling going on at different levels."
Several US officials told the newspaper they did not believe Israel had decided to attack Iran or think such a strike was imminent.
The UN Security Council has imposed several rounds of sanctions on Iran for defying council demands that it suspend its uranium enrichment program, which could be used to make fuel for power plants or atomic weapons.
Iran has refused to buckle to the sanctions and has spurned previous offers of economic benefits to suspend its uranium enrichment, which it says is to produce fuel for electrical power plants rather than for nuclear weapons.
Iran said Thursday it was ready to negotiate over a new package of economic incentives put forward by major powers seeking to persuade Tehran to curb its nuclear work.