Speaking to reporters at Parliament House on Thursday, Senator Lambie said she was seeking "legal and parliamentary advice" about her next move to ensure she had "every move covered", following a falling out with party leader Clive Palmer.

Mr Palmer launched an extraordinary attack on Senator Lambie on Wednesday, accusing her of lying to the Senate and plotting to set up her own political party.

Earlier in the day, the Tasmanian senator was demoted by her party for failing to attend party meetings.

The move comes after weeks of internal turmoil in the party and a war of words between Senator Lambie and Mr Palmer, with Senator Lambie complaining he was not doing enough on issues such as a better pay deal for Defence personnel.

Senator Lambie insisted on Thursday she was "absolutely not" a liar, but was coy about her intentions.

At one point, she seemed to suggest she would not form her own party, saying "that would be an overload for me".

She said she would spend the weekend in Tasmania consulting her constituents and mentors.

"I'll make a decision from there early next week," she said.

"I just want to do what I was elected to do. I just want to stay honest. I want my integrity to stay intact and I just want to get on with the job."

She committed to serving out her six-year Senate term.

"Absolutely, I'm here for the long run," she said.

In two radio interviews on Thursday, Mr Palmer repeated his claim that Senator Lambie had been plotting to set up another political party.

"It seems as though Jacqui's intent on establishing a new political party for veterans that she could be head of and one day, as she says, be Prime Minister," Mr Palmer told Devonport radio station 7AD.

"I don't personally think that's really achievable but we could achieve some change and protect our veterans if we all work together as a team," he said.

"So far Jacqui Lambie has not brought one proposal in respect of her beloved Tasmania before the party room or before the Parliament, nor has she brought one proposal in relation to veterans. It's not just about talking, it's about actually getting change."

On Wednesday, Senator Lambie posted a link on Facebook to the page of the Australian Defence Veterans Party, with no additional words or comments offered.

In a separate interview on Sydney's Triple M, Mr Palmer said it was "disappointing" Senator Lambie appeared to be preparing to leave the party.

"She got 22,000 votes in Tasmania above the line for Palmer United, and only obtained 1500 votes for herself as an individual. She really has a responsibility to represent those people," she said.

Mr Palmer said Senator Lambie was "persona non grata" in PUP "until she can get herself together".

Mr Palmer also said his party still had a deal with the Australian Motoring Enthusiast Party, despite its senator Ricky Muir on Wednesday breaking with the PUP position and joining Senator Lambie to disallow Coalition changes to financial advice laws.

Mr Palmer said under the agreement, Senator Muir had the right to vote independently from PUP on issues he felt strongly about.

"We've still got our deal with the Australian Motorists... They still have a voting arrangement with us that does give us the balance of power in the Senate," he said.

Speaking to reporters in Canberra on Thursday, Senator Lambie angrily rejected Mr Palmer's suggestion she had not achieved anything for her constituents.

"If Clive Palmer spent more time in Parliament he would see exactly what I've been doing," she said.

"I've sent out over 250 press releases in the last eight months, people have only got to go through Hansard to see what I've been saying and what I've been trying to do – I'm working an 18 hour day plus."