Hodgman backs Abbott as PM

Tasmania's Liberal premier has thrown his support behind federal leader Tony Abbott.

Will Hodgman says the federal coalition has served the island state well, with significant investment across multiple sectors, and he's declined to comment on whether current leadership speculation is damaging the Liberal party.

"The prime minister does have my support," he told reporters in Hobart on Monday.

Mr Hodgman said his focus was solely on Tasmania and refused to comment on criticism of the prime minister's performance.

"He has my support as indeed do my federal colleagues who have a keen interest in the state," Mr Hodgman said.

During a recent visit to Hobart Mr Abbott championed Tasmania's growth in tourism, investment and business confidence.

Mr Hodgman refused to comment on a hypothetical Malcolm Turnbull-led coalition.

"Tasmania has been served well by the federal government in recent years and significant investments in freight, irrigation, into key industry sectors ... are examples of a federal government delivering for the state," the premier said.