Premier Jeremy Rockliff issued an ultimatum to Liberals-turned-independents John Tucker and Lara Alexander on February 2, threatening the possibility of an early election if they did not agree.
The duo, whose decision to leave the Liberals in May plunged the government into minority, rejected the new deal which included a ban on supporting opposition bills.
On Friday, Mr Rockliff met with Mr Tucker and Ms Alexander, whose votes have propped up the government.
The premier said he would not ask the governor for an early election this weekend but did not rule out the prospect of a poll before Easter.
"I thank Mr Tucker and Ms Alexander for meeting with me," Mr Rockliff said in a statement.
"It was an opportunity for them to put forward their position, as I have mine."
Mr Rockliff said he would now take "the appropriate time to consider and to consult with my colleagues".
"This is an important matter," he said.
"Tasmanians need stability and certainty, and I am focused on delivering that."
Mr Tucker, who fronted media alongside Ms Alexander, indicated he had received some assurances from the premier.
He said the premier had agreed to abide by a parliamentary motion preventing any "shovels in the ground" for an AFL high-performance centre until plans for a new stadium passed parliament.
The new waterfront stadium was a condition of the AFL granting Tasmania a licence for inclusion in the competition, slated for 2028.
Mr Tucker said any flow-on impacts were a "question for the premier".
John Tucker and Lara Alexander's votes have propped up Tasmania's Rockliff government. (Loic Le Guilly/AAP PHOTOS)
In January, Mr Tucker threatened to "bring down the government" and move a no-confidence motion if the premier did not abide by the AFL high-performance motion and another to make CCTV mandatory in abattoirs.
Mr Tucker and Ms Alexander said their preference was to continue with their initial May agreement with the premier for ongoing votes of confidence and supply.
"I hope the discussions were conducted in good faith," Ms Alexander said.
"We have come here in good faith to resolve this crisis."
The state's Labor opposition said the premier had his "pants pulled down" by Mr Tucker.
"As if refusing to follow through on his threats after his ultimatum was rejected by the two independents wasn't embarrassing enough, Mr Rockliff is now giving in to Mr Tucker's demands to delay the AFL high-performance centre," Labor MP Josh Willie said.
"The premier is being held to ransom, but he's too weak to do anything about it."
Mr Tucker and Ms Alexander said the premier had given an assurance the trio would continue discussions late next week.
Parliament is scheduled to resume in early March, while the next election is not due until mid-2025.
Ms Alexander and Mr Tucker were concerned about government transparency around plans for an AFL team and stadium and the Marinus Link energy connector when they quit the Liberals.
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