Senator Hanson said she regretted the fact her legislation was necessary as she talked up vaccination side effects and unproven COVID-19 treatments.
"(It's a) pandemic of discrimination unleashed on the Australian people," she told the Senate when introducing her bill via videolink on Monday morning.
She took aim at state premiers for introducing mandates and adopted the prime minister's position about Australians having had a "gutful" of governments telling them what to do.
Senator Hanson also called Scott Morrison weak for not putting his money where his mouth is after he denounced mandates but would not legislate to remove state versions.
"If the prime minister is not happy with my bill then change it. You have the solicitor-general (to provide advice)," she said.
Queensland Nationals senator Matt Canavan also called vaccine mandates "unfair, cruel, unnecessary and unAustralian".
He said the bill would benefit with some amendments but he would vote for it regardless.
"I thought I was born in a free country," Senator Canavan said.
The government is facing an uphill battle in the Senate with Queensland senator Gerard Rennick and South Australian senator Alex Antic saying they would withhold their vote from all legislation unless mandates are scrapped.
Senator Hanson promised to cause "mayhem" for the government over the issue.
Finance Minister Simon Birmingham said the government would not seek to overhaul mandates.
"The government won't be dictated to, we will do as we've always done, which is work with our health advisors," Senator Birmingham told ABC radio on Monday.
"What I urge any parliamentarian to do is not to hold one issue to another unrelated issue, each piece of legislation ought to be considered on its merits."
Senator Rennick said while many jurisdictions had implemented mandates, he wanted the commonwealth to overrule state and territories.
"I feel as though the premiers have abused their trust and the trust of the people," he told Sky News.
"I don't think that the premiers have the power to mandate these vaccines and I would like the prime minister, to step up and and basically stop the overreach by the state premiers."
Treasurer Josh Frydenberg said discussions were ongoing with the disaffected senators over their mandate stance but the issue was for states and territories.
Opposition Leader Anthony Albanese accused Mr Morrison of pandering to extremists for not fully condemning violent demonstrators protesting the mandates.
"The prime minister should be capable of just showing leadership, not being weak, and saying these comments and this behaviour is unacceptable in Australia in 2020," Mr Albanese told ABC Radio.
"I hold the prime minister responsible for failing to call out unequivocally the violent and extreme comments that are made, the taking of gallows, the threatening of Labor MPs and premiers and independents."