Kahlon said on Hadashot TV news on Saturday that it was impossible to run a coalition with control of just 61 of parliament's 120 seats.
Kahlon's call was echoed by members of the nationalist Jewish Home whose head, Naftali Bennett, asked to succeed Lieberman as defence chief but was turned down by Netanyahu on Friday.
On Sunday, Israeli media reports said Netanyahu was now prepared to offer Bennett the post in a bid to keep Jewish Home in the coalition.
Such a move, the unconfirmed reports said, would also be aimed at forcing Kahlon to consider the risks to his own party, which also courts nationalist voters, in being portrayed as the main factor behind the collapse of a rightist government.
A poll published on Wednesday by Hadashot showed Likud falling from 30 to 29 parliamentary seats after months of polls that have shown it gaining power.
Only 17 percent of respondents were happy with Netanyahu's policy toward Gaza, where he agreed to a ceasefire - dubbed by Lieberman as "surrender" - after militants from its ruling Hamas group launched almost 500 rockets into Israel on Monday and Tuesday and Israel carried out dozens of air raids.
Netanyahu's re-election chances could also be affected by a series of corruption cases against him in which Israel's attorney-general is weighing his indictment.
An election would complicate promised moves by the United States towards reviving Israeli-Palestinian peace efforts that collapsed in 2014. The Trump administration has said it would unveil a peace plan soon.
