Ms O'Connor told State Parliament on Thursday that Mr Gutwein had "eased people's fears" about COVID-19.

"We're all receiving phone calls, emails of distress, we're going out into our communities and into empty streets and empty shops and we can feel that fear and uncertainty," she said.

"But there's been some things done by this government and this Premier that have eased people's fears.

"And I'll just say this. A really great friend of mine who's a raving greenie has developed a crush on you."

Ms O'Connor said there was a feeling that the Government and the Parliament had the community's back.

She commended Mr Gutwein for making tough decisions.

"We made the first moves on cruise ships, we worked to secure the borders better and now there's a suite of assistance measures in place for people who are made vulnerable through loss of employment, people who are tenants in the private rental market and in social housing, and for businesses," Ms O'Connor said.

Labor leader Rebecca White said people who were out of work had to wait too long for financial support from the federal government.

"The initiatives announced by the Premier today will assist to ease the pressure on households and businesses by limiting the bills they are required to fund out of their pocket," she said.

Leader of government business in the House of Assembly Michael Ferguson also paid tribute to his leader who he said needed everyone's full support.

Mr Ferguson applauded Mr Gutwein's work ethic and care for Tasmanians and said he was praying for Mr Gutwein and Prime Minister Scott Morrison.

Independent member for Clark Madeleine Ogilvie said Tasmanians recognised Mr Gutwein's strength.

"You have galvanised people," she said.