Braddon MP Miriam Beswick and Bass MP Rebekah Pentland will sit as independents in the lower house after being expelled on Saturday by the network founded by Tasmanian senator Jacqui Lambie.
The pair are among crossbenchers Premier Jeremy Rockliff's minority Liberal government relies on to stay in power after the March election.
In a bid to assuage fears of the Rockliff government collapsing, Ms Beswick and Ms Pentland issued a joint statement on Sunday.
"We are committed to providing the certainty and stability Tasmania deserves," they said.
"We will continue to offer the Rockliff government supply and confidence.
"We'll sign a new agreement with the premier in the coming days and share that agreement publicly once it's finalised."
Miriam Beswick and another MP will sit as independents after quitting the Jacqui Lambie Network. (Rob Blakers/AAP PHOTOS)
Mr Rockliff said he would make the new arrangement work.
"I pledged to work with the parliament that the Tasmanian people elected," he said.
"That's what I have done, and will continue to do.
"I will not resile from this, no matter how hard it gets or whatever challenges are thrown my way."
Ms Beswick and Ms Pentland "squandered" a golden opportunity to hold the government to account, their former party said.
"(They) have made it clear that they no longer represent the Jacqui Lambie Network's values of accountability, transparency and integrity," the party said.
Lyons MP Andrew Jenner will remain in the party.
Ms Beswick denied her values had changed.
"Our relationship with Jacqui has unfortunately deteriorated over the past few months and it's now best if we represent our electorates as independents," she said.
Ms Pentland said the pair rejected assertions they no longer stand for accountability, transparency and integrity as "they'll continue to guide every decision we make".
Jacqui Lambie's party says the MPs "squandered" an opportunity to hold the government to account. (Lukas Coch/AAP PHOTOS)
Labor Opposition Leader Dean Winter said his party had been "expecting the implosion" of the party, also known as JLN.
"Jeremy Rockliff has been talking up minority government but the stability he promised is already gone," he said.
One condition of JLN agreeing to prop up the Liberal government, in power since 2014, was a deal for an independent report into the state's finances.
Economist Saul Eslake's analysis painted a bleak picture of the state's budget and found the Liberal government was "entirely to blame" for the state's economic deterioration.
He estimated net debt would rise to more than $16 billion in 2034/35, more than 25 per cent of gross state product, unless tax reform is implemented.
The report looming large over parliament's return in a fortnight, with the government due to respond when the budget is delivered on September 12.
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