Netanyahu, who won a fourth term last year, governs by a majority of one in the 120-member Knesset, making his administration vulnerable to any falling-out among his political allies, so he is keen to add to their ranks.
It had appeared for the past several days that a course had been set for Isaac Herzog's centre-left Zionist Union party, which has 24 lawmakers, to agree on an alliance with Netanyahu's right-wing Likud.
But in a surprise move, Lieberman, who heads the far-right Yisrael Beitenu party and previously served as foreign minister, convened a news conference on Wednesday to say he was ready to negotiate a pact with Netanyahu.
Lieberman, whose party has six Knesset seats, demanded the defence portfolio as well as new legislation that would impose capital punishment on Palestinians carrying out fatal attacks.
While saying Netanyahu acquiesced to Lieberman's demand to be appointed defence minister, the political sources, who spoke on condition of anonymity, noted that other issues remained unresolved and a deal has yet to be finalized.
Lieberman, who twice served as foreign minister in previous Netanyahu-led governments and has had testy relationship with the prime minister, has drawn headlines by repeatedly questioning the loyalty of Israel's Arab minority.
In the past, he has proposed transferring some Israeli Arab towns to a future Palestinian state in return for Jewish settlements in the Israeli-occupied West Bank.
After hearing of the Lieberman-Netanyahu meeting, Herzog froze his own talks with the premier. In a speech televised in prime time, Herzog said that bringing in Lieberman would lead to a government whose "policies are on the brink of madness".
If appointed, Lieberman would replace Moshe Yaalon, a Likud member and former armed forces chief.
Yaalon has drawn sharp criticism from far-right partners in Netanyahu's coalition for backing the army's decision to level manslaughter charges against a soldier who shot dead a wounded Palestinian attacker in the West Bank in March.
Enlisting the Zionist Union, which has 24 legislators, would have given Netanyahu a comfortable political cushion and put a more moderate face on his right-wing government at a time when Israeli is grappling with mounting international calls to renew peace talks with the Palestinians that collapsed in 2014.
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