Labor parliamentarians on Wednesday held a two-hour meeting in the opposition's office in Parliament House to discuss the leadership after former leader David O'Byrne officially tendered his resignation.

This resignation, forced by publicity around sexual harassment allegations from his time as a union boss about 14 years ago, came three weeks after he took the leadership.

Ms White stood for the leadership unopposed.

Former leadership aspirant Shane Broad was believed to have been considering standing for the position, but told media before the meeting he would support Ms White's nomination.

Deputy leader Anita Dow retained her position.

It is believed it was discussed at the meeting that Ms Dow should step aside to make way for Dr Broad, but she refused to do so.

Ms White told media after the meeting the party's internal destabilisation had to end.

"There is a very clear view around our table that we want to be able to work together now," she said.

"The backgrounding in the media, the stories that we've been hearing have to end.

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"I'm confident from the conversations I've had over the past couple of days that there is goodwill to make sure that we do work together, that we don't continue to undermine one another."

Ms White said the backroom disunity had been detrimental to both the labour movement and the Tasmanian community.

"They haven't had a good opposition and we need to have a strong opposition to hold the government to account," she said.

"There will be some time needed for us to address some of the challenges we see in the Labor Party and I ask the community to please have some patience with us."

Ms White stood down from the leadership in May following two consecutive election loses.

Labor insiders had said that she did not want to relinquish the leadership, but had bowed to pressure factional heavyweights who wanted to see Mr O'Byrne installed into the position.

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Fifteen days into the leadership, it emerged that the party's executive had received a complaint against him from when he was head of the Liquor, Hospitality and Miscellaneous Union.

A former female employee had said he had sent her unwanted text messages of a sexual nature and twice kissed her without consent.

Mr O'Byrne last month said he had believed the contact was consensual.

Ms White said the party's investigation still needed to take its course.

"I haven't seen the complainant's accusations - that's for the investigator to consider," she said.

Ms Dow will be acting leader of the party until Ms White returns from parental leave next month.

If Labor's internal issues have been resolved, it's now time to get on with the job.

That's the view of former Labor minister and political commentator Julian Amos.

Dr Amos on Wednesday said the fall of David O'Byrne was a tragedy for himself and the party.

"It was Shakespearean in its context," he said.

"Once these things happen, they have to resolve themselves and I think they've done it quickly and incisively."

Premier Peter Gutwein said Labor's decision to return to Ms White as leader showed the party's lack of talent in the House of Assembly.

"It is simply inconceivable that Labor have no other options," he said.

"It speaks volumes that less than two months after dumping Ms White as leader, the Labor caucus has come crawling back and re-endorsed her," he said.

Greens spokeswoman Rosalie Woodruff said Ms White failed to make strong policy decisions in her time as leader and played a small target strategy from the opposition benches.

"They have not had any strong points of differentiation from the Liberals in government," she said.

"That means Tasmanians have effectively had a failed opposition."

People within the party last week were calling for Ms White to return to the leadership, saying that Mr O'Byrne's position was untenable.

They said he had undermined her leadership since his return to Parliament in 2018 along with figures in the union movement.

They said Shane Broad, favoured by the right, should be deputy leader.

Labor sources and former leaders when contacted on Wednesday about Ms White's return to the leadership did not respond to calls for comment or declined to do so.