Following a lively debate at the International Atomic Energy Agency's annual general conference, the measure, supported by Iran, was defeated by 51 votes against and 43 in favour with 32 abstentions.
Israel is widely assumed to have nuclear weapons but has never acknowledged it and is not a signatory to the landmark Treaty on the Non-Proliferation of Nuclear Weapons (NPT).
The Jewish state is a member of the International Atomic Energy Agency but is not subject to IAEA inspections except for at a small research facility.
In 2009 the same resolution was narrowly approved by members of the IAEA and in 2010 it was defeated only after intensive lobbying efforts by Western countries.
In 2012 and in 2011 Arab states decided not to propose the resolution in order to encourage the creation of a Middle East free of weapons of mass destruction.
These efforts, however, have so far come to nothing, with a hoped-for conference failing to take place in late 2012 as planned.
Oman's ambassador Badr Mohamed Zaher Al Hinai, talking on behalf of Arab states at the IAEA, said that the proposed resolution "could resuscitate" efforts towards a nuclear-free Middle East.
Attacking the "double standards" of Western countries, he called allegations that other Middle East countries were seeking nuclear weapons a "huge distortion of the facts".
Speaking for Israel, deputy ambassador Daniel Danieli said that the resolution amounted to "Israel-bashing" that "contributes to the politicisation of the IAEA.
