JERUSALEM — If there was any doubt about the degree of cooperation between the top military brass of Israel and the United States, the coming month should put those doubts to rest.

Gen. Martin Dempsey, the chairman of the Joint Chiefs of Staff, landed in Tel Aviv on Sunday to launch "Austere Challenge 12," the largest-scale joint military exercise Israel and the United States have ever undertaken, at a cost of $38 million to the two nations.

Dempsey’s arrival came just two months after he provoked controversy by saying he did not “want to be complicit” if Israel chose to bomb Iran’s nuclear facilities on its own. At the time, his comment illustrated the deteriorating relations between the governments of Prime Minister Benjamin Netanyahu and President Barack Obama, who had fallen out (at least moreso than usual) over the issue of Iran.

At least publicly, that fallout was not on display when Dempsey landed on Sunday. The general made a a meeting with the Israeli Defense Minister Ehud Barak his first stop, emerging at about midnight. A well-choreographed series of photo-ops followed, including one with Israel's president. But at the core of the 48-hour visit was the most extensive collaboration ever tested between the two armed forces.

Capt. Eytan Buchman, an Israeli army spokesman, confirmed that only the most superficial details of the visit are being shared with the media. Still, he added, "we are in the middle of the biggest drill we have ever done. So I'd say it stands to reason that their commanders want to see how it is going."

About 3,500 US troops are participating in the three-week-long drill, which was originally scheduled for last spring, but was postponed and modified.

Some opponents of Obama are questioning the drill’s timing.

"It is highly unusual for a Chairman of the Joint Chiefs of Staff to personally attend US military exercises," said J.D Gordon, a former Pentagon spokesman in the Bush Administration.

In a Pentagon briefing last week, Lt. Gen. Craig Franklin, commander of the Third Air Force, dismissed the accusation that the visit was pegged to the election.

“AC12 is not related to election cycles, or any perceived tensions in the Middle East,” he said. “We are military professionals coming together to train for a defensive mission. AC12 is another step as our continued military cooperation moves forward."

Shlomo Brom, a retired Israeli Brigadier General, said that whatever the political message, the troops involved "definitely need practice.”

“The idea that in an emergency two very different anti-missile systems or radar systems will work together is not trivial. Both land and sea-based anti-missile systems have to be in sync. It is very complicated. You simply need to practice. So, the drill itself is important," he said.

Still, Brom did think the drill held an underlying message — to Iran. The message that the United States and Israel are full partners and that should the need arise, the United States will guarantee Israel's safety is self-evident, he said. "In this case, I think Tehran is the principal target for this message, though this is not new.”

The joint military exercise came just as Iran sent two warships to dock off the coast of Sudan. Sudanese officials said the Iranian ships had arrived as a show of solidarity between the two countries, a week after Sudan blamed Israel for striking a weapons depot in Khartoum.

Still, Gordon, the former Bush administration Pentagon spokesman, said he thought Obama was maneuvering politically, not diplomatically.

"This is more about a drill for the US elections than stopping Iran," he said.

"President Obama has had a strained relationship with Prime Minister Netanyahu since the early days of the administration when he skipped visiting Israel on a Middle East tour of four countries, including Egypt and Saudi Arabia, while also not doing enough to stop Iran's nuclear program. These large scale drills are simply a last ditch effort to mute criticism on both fronts, otherwise we would have been doing them for years, instead of a week before elections."

Austere Challenge 12 is considerably larger than previously held drills, he says, and may even include German and British forces. Joining Dempsey is the chief of the US military’s European Command, Adm. James Stavridis.