Lieberman however said he had no intention of starting a new war in Gaza, which would be the fourth since 2008.
He urged Palestinians to pressure Hamas, the Islamist movement that runs the Gaza Strip, to "stop your crazy policies".
"As minister of defence, I would like to clarify that we have no intention of starting a new war against our neighbours in the Gaza Strip or the West Bank, Lebanon or Syria," he said in the interview with Jerusalem-based Al-Quds newspaper.
Lieberman is part of what is seen as the most right-wing government in Israeli history, with several prominent members of Prime Minister Benjamin Netanyahu's coalition openly opposing a Palestinian state.
But while known as a security-minded hardliner, Lieberman believes in a two-state solution to the conflict based on land swaps.
He reiterated that position in the interview, saying he sees the main settlement blocks in the occupied West Bank remaining part of Israel under a final peace deal.
He predicted Abbas would lose if elections were held, with polls showing most Palestinians would like the 81-year-old to resign.
Such elections could lead to Hamas taking power in the West Bank, where Abbas's secular Fatah party currently dominates, but Lieberman said he believed a different outcome was possible.
"There are enough sensible people in the (Palestinian Authority) who understand the situation and know if there is a choice to make between Hamas and Israel, they think partnering with Israel will be better for them," he said.
Al-Quds was heavily criticised on social media by Palestinians who say it should not have agreed to an interview with an Israeli official as it amounted to sanctioning "normalisation" with an occupying power.
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