The conservative Liberal government, led by Premier Jeremy Rockliff, was on track to win the most seats in the new parliament but likely fall short of a majority after Saturday's election, the Australian Broadcasting Corp reported.
The election was sparked after defections from Rockliff's party plunged the only Liberal government among Australia's six states and two self-governing territories into minority.
Rockliff told reporters that voters had given the Liberals "a mandate to form a new government".
"We've won the most seats and indeed the most votes and so the Tasmanian people have not voted to change the government," he said in the state capital, Hobart.
Opposition centre-left Labor leader Rebecca White has not conceded defeat said late on Saturday it would likely be a "long few weeks until we know the exact makeup of the next parliament".
Australia's Deputy Prime Minister Richard Marles said on Sunday the Liberals had suffered a 12% swing against them in the poll. He said the federal Labor government would work with "whoever forms government in Tasmania".
Tasmania is a one-hour flight or 10-hour ferry crossing from the mainland city of Melbourne, 445 km (275 miles) away. Forty percent of the island is wilderness or protected areas.
It is the only Australian state that uses proportional representation to elect its lower house and has a long history of minority governments.
(Reporting by Sam McKeith in Sydney; Editing by Jonathan Oatis and William Mallard)
