The Israeli and U.S. have likely dropped the plan of a large-scale joint exercise initially scheduled in May, Israel's Army Radio reported Sunday.

Thousands of U.S. troops were due to be deployed in Israel for the largest-ever joint maneuver in the allies' history, dubbed " Austere Challenge 12," during which they were to test their air defenses against ballistic missiles.

The Israel Air Force planned to test its gamut of counter- missile and rocket systems, including Iron Dome, Arrow, Magic Wand and the U.S.-made Patriot. The U.S. was to bring along THAAD, a system for intercepting high-altitude missiles, as well as other hi-tech weapons platforms.

Army Radio quoted Israeli defense sources as saying that the main consideration behind the cancellation was the fear that the drill would potentially "create unnecessary headlines" at a time of increased tensions over recent Iranian threats to block the Strait of Hormuz, a strategic shipping channel linking the Gulf and the Arabian Sea.

Earlier Sunday, however, Israel Radio reported that the maneuver has only been delayed after Israeli defense officials last month cited budgetary constraints during the meetings with their U.S. counterparts, and that both sides agreed to reschedule the drill for the last quarter of 2012.

While an official statement has not yet been issued, an Israeli defense ministry spokesman said that discussions on the matter are still going on and no final decision has been made.

"The possibility that the drill will be canceled is not connected in any way to budgetary issues. Whether or not it will be held depends on the level of sensitivity and the amount of resources it will require," Army Radio quoted a defense official as saying.

Meanwhile, Gen. Martin Dempsey, chairman of the U.S. Joint Chiefs of Staff, is due to arrive in Israel later this week for meetings with Defense Minister Ehud Barak, Israeli army Chief of Staff Lt.-Gen. Benny Gantz and other top defense and intelligence officials.

Observers said the visit aims to both coordinate strategy over Tehran's nuclear program and to assess Israel's intentions regarding a potential military strike on the Islamic Republic's nuclear facilities in the near future.

Dempsey and U.S. Secretary of Defense Leon Panetta have said in recent interviews that Israel would likely launch such an attack without prior coordination with the United States.

U.S. President Barack Obama had warned Israeli Prime Minister Benjamin Netanyahu of the consequences of military actions in a phone conversation on Thursday, The Wall Street Journal reported.

The two leaders are at odds over the so-called "red lines", which would justify an attack, regarding Iran's nuclear activities, the journal said.

Israeli officials last week noted the progression of work in a uranium enrichment facility near Qom was a crossing of a red line, while Panetta disagreed and said the U.S. would not tolerate the closing the Hormuz.

According to the Journal, the United States is drawing up contingency plans to protect its military installations and forces in the Middle East and the Gulf in case Israel were to launch a strike.