He has strongly denied the accusations and has flagged legal action against certain individuals and organisations for making what he maintains are false claims about his private life.
Gutwein, whose party claimed the seats required to govern in majority on Wednesday night, has stood by Brooks and brushed off suggestions the matter was a gender issue.
“Adam has emphatically denied these matters and I take him at his word,” Gutwein said.
“This is not a gender matter. If Mr Brooks were gay, and two men had made these claims, my position would be exactly the same.”
Gutwein described the allegations as “obviously concerning” and said he would weigh up cabinet positions over the weekend once the final make-up of parliament was decided.
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Tasmania s Liberal Party has secured a majority government by winning a crucial 13th seat in the state s lower house.
After a lengthy wait following the 1 May poll, preference distributions delivered the seat in the Hobart-based electorate of Clark to Liberal Madeleine Ogilvie on Wednesday night.
Premier Peter Gutwein, who claimed victory on election night, had pledged to step down if the party couldn t secure majority in the 25-member lower house.
Ms Ogilvie, a former Labor MP and independent, was among a field of four candidates jostling for two in-doubt seats in Clark.
Under Tasmania s Hare-Clark voting system, five MPs are elected in each of the state s five electorates.
Counting continues after the weekend election in Tasmania, with Liberal Premier Peter Gutwein reiterating he'll stand down if his party doesn't secure majority.