The survey by Nippon Television Network coincided with weekend rallies by thousands protesting the legislation, which would allow Japan to exercise its right of collective self-defense, or militarily aiding a friendly country under attack.
Abe's cabinet adopted a resolution last July reinterpreting the pacifist constitution to allow the dramatic shift in security policy. In April, Abe told the US Congress that the changes, already reflected in new US-Japan defense cooperation guidelines, would be enacted this summer.
But the outlook for passage in the current session of parliament, set to end next week but which may be extended until early August, has been clouded by growing criticism that the legislation violates the pacifist constitution, drafted by US officials after World War Two.
Abe's support slipped to 41.1% from 43.5% in the Nippon Television survey, which also showed 62.5% were opposed to the exercise of collective self-defense and 63.7% were against the enactment of the legislation in the current session of parliament. Almost 80 percent felt the government has not explained the legislation sufficiently.
A majority - 56.2% - also said the government's "Abenomics" recipe for reviving the economy with hyper-easy monetary policy, spending and structural reforms was not going well.
Thousands of Japanese rallied on the weekend to protest the security bills and other government policies such as plans to restart nuclear reactors taken off-line after the March 2011 Fukushima nuclear disaster.