The 585kg lander will make its way to the Moon under its own power and is expected to arrive in orbit on 4 April before heading to a soft landing on 11 April.
Simply making it to the moon, however, would be a historic achievement, as Beresheet would be the first non-government craft to reach the lunar surface.
The Israeli team said glare from the sun on the spacecraft's sensors was making it more hard than expected for the spacecraft to orient itself according to the position of the stars as it prepared for its first orbit around the Earth, the first stage of its slow seven-week journey to the moon.
The 585-kilogram, dishwasher-sized lander was built by Israeli nonprofit space venture SpaceIL and state-owned defence contractor Israel Aerospace Industries (IAI) with $US100 million furnished nearly entirely by private donors.
The company pulled off the crowd-pleasing stunt of landing the booster back on SpaceX's "Of course I still love you" drone ship less than nine minutes after lift-off.
For Israel, the landing itself is the main mission, but the spacecraft also carries a scientific instrument to measure the lunar magnetic field, which will help understanding of the Moon's formation.
"It's a big step for Israel but a giant step for Israeli technology".
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The US Apollo program tallied six manned missions to the moon - the only ones yet achieved - between 1969 and 1972, with about a dozen more robotic landings combined by the Americans and Soviets. The $100 million Beresheet mission couldn't afford its own rocket - even a little one - so the organizers opted for a ride share.
"This is Uber-style space exploration, so we're riding shotgun on the rocket", Winetraub explained at a news conference on the eve of launch.
The unmanned robotic lander dubbed Beresheet - Hebrew for the biblical phrase "in the beginning" - was due for liftoff at 8:45 p.m. EST (0145 GMT Friday) atop a Falcon 9 rocket launched by California-based entrepreneur Elon Musk's SpaceX company from Cape Canaveral Air Force Station.
Once planted on the Moon, Beresheet will transmit photos and videos back to Earth, per SpaceNews. The other two items taken up were an Indonesian communications satellite and a US Air Force experimental satellite.
To save on fuel, the spacecraft is taking a more convoluted route to the Moon than usual. NASA has a laser reflector aboard Beresheet and is offering its Deep Space Network for communication.
The spacecraft will also plop the Israeli flag on the lunar surface and take some snaps before the mission ends two days later.
Musk said the booster will fly a fourth time in April, during a launch abort test of the new crew Dragon capsule.