Although Israeli Prime Minister Benjamin Netanyahu and President Obama have had a strained relationship, rubbed raw by their deep disagreement over the Iran nuclear deal, U.S. ­spending on Israel’s air defenses has soared in the past decade, from $133 million in 2006 to $619 million in 2015.

[A photograph provided by the Israeli Ministry of Defense shows a launch of the David’s Sling missile defense system. (Israeli Ministry of Defense/Associated Press)]

The Israeli defense establishment and its American partners have designed a layered system that will allow the Jewish state to respond to simultaneous attacks from multiple fronts — the relatively crude homemade rockets lobbed by Hamas from the Gaza Strip, the midrange rockets and missiles fired by the Shiite militants of Hezbollah from Lebanon, and the long-range ballistic missiles being developed by Iran that could carry conventional or chemical warheads.

In addition, Israel’s new X-Band radar will allow its forces to detect incoming missiles 500 or 600 miles out, vs. 100 miles, the current limit of their radar tracking systems, according to summaries of the systems provided to Congress.

“I define the system as pioneering,” said Uzi Rubin, former head director of Israel’s missile defense program. “Even the United States doesn’t have anything as complex, as sophisticated.”

The system will also be able to prioritize incoming rockets and missiles by calculating their trajectories. Some missiles may not be intercepted, if their targets are fields and farms, but projectiles that would hit populated areas or important infrastructure — such as military bases, oil refineries and nuclear facilities — would be stopped.

The Israeli missile defense system is being built in partnership with U.S. defense contractors, including Raytheon, Boeing and Lockheed Martin.

The Israelis are planning to start deploying their coordinated system of radars, launchers and interceptors over the coming months, though there have been delays in the past, they warn.

In December, Israel and the U.S. Missile Defense Agency celebrated successful tests of two new ballistic missile defense systems — David’s Sling, which is designed to intercept short- and medium-range threats, and ­Arrow-3, which is intended to stop long-range attacks and knock out enemy targets in space by deploying “kamikaze satellites,” or “kill vehicles,” that track their targets.

David’s Sling and Arrow-3 will join Iron Dome and the existing Arrow-2 in coming months.

The Iron Dome batteries were responsible for intercepting 90 percent of their targets during Israel’s war with Hamas in the summer of 2014, according to the Israel Defense Forces, when Hamas fired 4,000 rockets and mortar rounds at Israel from the adjacent Gaza Strip.

On Tuesday, the Defense Ministry announced that major components of the David’s Sling defense system will be delivered to the Israeli air force “over the course of several weeks.”

Israel called David’s Sling “the world’s most revolutionary innovation in the family of interceptor systems.” The system is designed primarily to handle the kinds of rockets and missiles, built by Iran and Russia, that are now in the possession of the Hezbollah militia in Lebanon and the Syrian regime of Bashar al-Assad.

Beyond the threat posed by the splintering of Syria, Israel is worried that Syrian missiles could be transferred to Hezbollah or acquired by the Islamic State or al-Qaeda.

In a recent speech, Hezbollah leader Hasan Nasrallah threatened that his militia’s missiles could strike ammonia storage tanks in Israel’s Haifa port in a future showdown with Israel, warning that the damage would be equivalent to an atomic bomb and could kill 800,000 people.

Maj. Gen. Nitzan Alon, the ­Israel Defense Forces head of operations, said Hezbollah could have upward of 100,000 rockets and missiles stored in Lebanon.

In 2006, before the deployment of Iron Dome, Hezbollah fired about 4,000 projectiles at Israel’s northern cities, causing some 40 civilian deaths and significant damage.

Israel’s military leaders warn civilians that no air defense ­system is perfect — or even close to it.

“There is no hermetic defense or total security that will intercept everything fired at Israel. In the next real war, rockets will fall on the State of Israel,” said Brig. Gen. Zvika Haimovich, commander of the Israeli air force’s Aerial Defense Division.

Haimovich briefed reporters last week in the middle of “Juniper Cobra,” a biennial U.S.-Israel air defense drill, which is scheduled to end Thursday.

More than 1,700 U.S. soldiers and sailors, alongside American civilians and contractors, are taking part in the exercise, which ­is focused on computer simulations of coordinated and sustained air attacks on Israel from multiple fronts.

In such a scenario, U.S. air defense probably would come into play, and the drill is designed not only to test Israel’s soon-to-be-deployed systems but also to improve how well U.S. and Israeli assets can communicate and coordinate their response.

“The purpose of this exercise is to improve interoperability of our air defense forces and our combined ability to defend against air and missile attack,” said Lt. Gen. Timothy Ray, U.S 3rd Air Force commander.

“And just as important,” Ray said, “it signals our resolve to support Israel and strive for peace in the Middle East.”

Booth reported from Jerusalem.