The Israeli military says the systems are needed to protect the country from massive missile bombardment until 2015.
The move comes amid growing concerns in Israel, fueled to a large extent by strident warnings from generals and more recently Prime Minister Binyamin Netanyahu, that the Jewish state is increasingly vulnerable to bombardment by tens of thousands of missiles and rockets held by Iran, Syria, Hezbollah in Lebanon and Palestinian militants in the Gaza Strip.
All this has emerged as Netanyahu has been forced to reduce Israeli the military budget to boost social spending after months of protests in 2011.
At the same time, the U.S. administration has made major cuts in the Pentagon's budget because of economic woes.
U.S. President Barack Obama has pledged that Washington won't jeopardize Israel's defense capabilities but at the same time he's been leaning on Netanyahu to hold off any unilateral Israeli attack on Iran's nuclear program, which Netanyahu claims is an existential threat to the Jewish state.
The feeling in Israel, and quite a few people in Washington as well, is that Netanyahu's seeking to squeeze extra funds out of Obama by exploiting U.S. concerns the Americans will be dragged into another Middle East war if Israel does strike.
Israel's Ynet Web site, the online service of the Yediot Ahronot daily, quoted Israeli sources "privy to the deal" as saying the two sides are discussing the proposed aid package.
Indeed, Ynet acknowledged that "the U.S. Congress and administration's apparent willingness to allocate the funds may be seen as an attempt to incentivize Israel to delay its decision vis-a-vis a military strike on Iranian nuclear facilities."
If approved, the requested U.S. funding would allow Israel to build four additional batteries of the Iron Dome system developed by state-owned Rafael Advanced Defense Systems and speed up work on another air-defense weapon, David's Sling, also being developed by Rafael.
The United States provided $205 million fiscal 2011 to help fund Iron Dome.
In March, a bipartisan group introduced the Iron Dome Support Act in Congress authorizing the administration to provide more funds for the system as required by Israel.
Obama has said he'll provide "an appropriate level of funding," and that presumably will cover whatever sum the administration decides on in the coming days.
Iron Dome, which got its baptism of fire against Palestinian Qassam and Grad rockets in 2011, is designed to intercept short-range rockets and missiles. It's able to down 76 percent of the projectiles it engages.
But there are only four batteries, each costing in excess of $50 million, deployed. Military planners say at least 20 are needed to cover all of Israel against short-range missile fire from Lebanon and the Gaza Strip.
Three are in the southern Negev Desert facing Palestinian rockets fired from Gaza. The fourth was deployed two weeks ago near Tel Aviv, Israel's largest urban area.
Rafael said in March the government has ordered seven units.
There have been reports Rafael is seeking to extend the range of Iron Dome's rocket interceptors to 155 miles on the premise that fewer batteries would be needed.
David's Sling is intended to counter missiles with a range of up to 70 miles as well as cruise missiles.
These two systems comprise the lower tiers of a planned four-level missile defense shield.
The two top layers will be high-altitude Arrow-2 and Arrow-3 systems developed by state-owned Israel Aerospace Industries to counter ballistic missiles such as Iran's Shehab-3b and Sejjil-2 and Syria's Soviet-designed Scud-C and M600 weapons.
Arrow-3, under development by IAI and Boeing, is designed to intercept such missiles at long-range beyond Earth's atmosphere.
The entire Arrow program has been largely funded by the Americans since the 1990s.
For now, the primary concern is to rush as many batteries of Iron Dome into operational deployment as fast as possible.
The firing of three Grad rockets at the southern resort city of Eilat on the Gulf of Aqaba from the Sinai Peninsula at late Wednesday opened up a new threat.
It wasn't clear who unleashed the rockets but Palestinian fire has until now come from the Gaza Strip further north on the Mediterranean.
Notable deaths of 2014 [PHOTOS]