Yaalon, forced out in May to allow Netanyahu to expand his coalition by bringing in a hardline nationalist party, has repeatedly criticised the government since leaving office.
"The current leadership must stop scaring citizens as if we are on the verge of a second Holocaust," Yaalon told a security conference in Herzliya, stressing threats were being exaggerated.
Israel "deserves a leadership that stops zigzagging and encouraging hate between different groups in Israeli society to remain in power at any price," he added.
In the remarks broadcast online, Yaalon said "my intent is to run for the leadership of Israel in the next elections" which are due to take place in 2019 at the latest.
Netanyahu dismissed the remarks of his former defence minister.
"These statements have no importance whatsoever," the prime minister told reporters.
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"Security is a real issue and Israel cannot ignore threats."
There has been speculation that a new centre-right party could be formed, with polls showing that one including Yaalon could pose a challenge to the Likud party, to which he and Netanyahu belong.
When he resigned last month, Yaalon warned of a rising tide of extremists in the country as well as in Likud.
Yaalon, also a former armed forces chief, had repeatedly clashed with far-right members of the coalition before resigning.
One high-profile dispute saw Yaalon and top military brass strongly condemn a soldier who was caught on video shooting a Palestinian assailant in the head as he lay on the ground posing no apparent threat.
Far-right politicians and protesters defended the soldier, who is currently facing a military trial for manslaughter.
Yaalon was replaced as defence minister by Avigdor Lieberman, a hardliner who has spoken of harsh actions against Palestinian "terrorists".
Yaalon was seen as a counterweight to religious nationalists who hold key positions in Netanyahu's right-wing cabinet, though he has in the past voiced opposition to a Palestinian state.