"There is no doubt that the certainty, the stability, the common purpose, the plan that we've outlined is best delivered by majority government and certainly the record shows, best done by Liberals," he told reporters at New Norfolk.
"I believe fundamentally that Tasmanians trust me and my team to deliver on what we promised, we have a strong plan for our state's future."
The Liberals hold a majority of 15 seats in parliament but Labor under Rebecca White is expected to put up a stiff fight with many analysts tipping a hung parliament scenario that could see the balance of power fall in the hands of the Greens or the Jacqui Lambie Network.
Mr Hodgman labelled it a "crucial election", warning that the last time there was a minority government the state's unemployment rate "skyrocketed" and jobs were lost.
He ruled out any deals with the Greens or the Jacqui Lambie Network.
"We will govern alone or not at all," he said.
"We'll be campaigning every single day to demonstrate why that is so, and why the risk of going back to the political uncertainty and instability of the hung parliament will not be in the state's best interests."
Ms White says Labor, too, will be campaigning for a majority government and believes it has the team and policies to win.
"It's been my sole focus to campaign for majority Labor government because I know Tasmanians deserve better than Will Hodgman and his team," she told reporters in Hobart.
"We will not do any deals with any minor parties. We will not do any deals with the Greens. And we will not govern in minority."
Ms White, who has been opposition leader for barely 12 months, brushed off suggestions her future hangs on victory at this election, declaring she was "not going anywhere".
She said health was the No.1 issue for many Tasmanians and will be Labor's priority if elected.
Tasmania Greens leader Cassy O'Connor said her party has not had any discussions with either major party about forming a minority government.
It was up to Tasmanians to decide the make-up of the next parliament, she said.
"If they decide that no party should be given a majority, we'll be there working for stable government, cooperatively and constructively," she told reporters.
"We say that minority government is government for grown-ups and majority government is for vested interests, corruption and corporate deals."
The Greens will be campaigning for five seats, but Ms O'Connor admits it will be tough.
"It's going to be a very dynamic and fluid election, but we're ready."