The Tasmanian Premier has been forced to apologise to the state's Opposition Leader for suggesting he "slit his wrists".

The throwaway line came after Will Hodgman sat down after a speech in State Parliament this morning.

Mr Hodgman had just resumed his seat after talking about the state's tourism boom.

He was not addressing Parliament but was overheard on Tasmania's parliamentary video feed saying "slit your wrists mate".

Mr Hodgman apologised for the quip at a press conference a short time later.

"I did make a silly comment to Bryan Green, I apologise for it," he said.

"In the heat of the moment these things occur and I apologise for it.

"The usual rough and tumble of Parliament often causes all members of the place to say things they perhaps shouldn't."

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Mr Green said it was especially disappointing given the State Government had launched a suicide prevention strategy last week.

"It's a terribly insensitive thing to say to anyone, let alone me, just four days after you've released a policy in relation to suicide prevention,' he said.

But he stopped short of calling for any further action against the Premier.

"In the end it's a public judgment," he said.

"I think that people within the community will be outraged that the Premier of Tasmania would say such a thing."

Mr Green said he accepted a personal apology from Mr Hodgman after the incident.

The comment has caused a social media backlash with some calling the comments a disgrace and others asking for the Premier to resign.

One person suggested the Premier should donate some of his salary to Lifeline.

Greens leader Cassy O'Connor said suicide was an issue which should be above politics.

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"It's completely inappropriate, it was a terrible use of language about a subject which is fraught, highly emotional and complex," she said.

"It's a very unfortunate juxtaposition after the Government last week produced a very sound suicide prevention strategy."

Ms O'Connor said she was disappointed in the comments, as others who were affected by suicide would be.

"For some people who are still grieving it will be a reminder of that terrible, terrible pain, I hope that they feel somewhat reassured by the fact that he has immediately apologised and is obviously sorry about what he has said."

Anyone who needs help is advised to call Lifeline on 13 11 14.