And she has also called on Prime Minister Tony Abbott to reconsider fellow Tasmanian Eric Abetz's position as government leader in the Senate.

Senator Lambie quit Clive Palmer's party last November after repeatedly clashing with the party's founder. She argued at the time that being a member of the PUP had prevented her from voting in the Senate in a way that she felt was best for Tasmanians.

On Friday, hours after Senator Lazarus announced that he, too, had quit the disintegrating Palmer bloc, Senator Lambie said she had been attempting to mend fences with the Queenslander and WA PUP senator Zhenya "Dio" Wang.

"They were angry when I left but they have turned around in the last month or so, as I've tried to mends things," she said.

She would not rule out forming a new voting bloc with Lazarus, and potentially other crossbench senators, to increase their negotiating power.

"I'll do whatever makes good decisions for the nation," she said, adding that "a lot of the crossbench have similar morals and views".

"Whether independent or with a party, he [Lazarus] is big enough to stand on his two feet."

The defection of Senator Lazarus means there are effectively now eight independent-minded senators on the crossbench for the government to negotiate with.

Senator Lambie said that she had heard Senator Abetz saying negotiations would be more difficult now for the government.

"The only person making it more difficult is Eric Abetz. I think it's about time they had a look at their Senate leader - he creates problems."

The senator said she did not know the details of what had happened to precipitate Senator Lazarus' exit, but that the senator and Ms Lazarus were a tight-knit family.

"I wish Laz good luck. I could see it shifting in the last month, there were pressures in the background and Clive is difficult to deal with."

"The pressure from Clive can be really difficult, but it is hard to pull the pin."

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