Senator Parry, a Tasmanian Liberal senator, told a Senate estimates hearing that he was forced to cancel a trip to the United States and Canada three days out from take off because he was waiting to get the go ahead by Mr Abbott's chief of staff Peta Credlin.

The president is allowed five uncapped overseas trips per year, and he said the convention had been that the prime minister's office would approve them, or give them ''concurrence'', without question.

But he told the committee Mr Abbott's office began querying aspects of some trips. 

He said he had not received approval for the trip three days out from take off, and was forced to cancel it.

''We had a lot of things on standby, but it became too late, so we cancelled the travel,'' Senator Parry said.

''It made life a little bit difficult, especially with the work that the post had done twice on this same travel,'' he said.

Mr Abbott's chief of staff did eventually grant Senator Parry approval, but it was too late.

Senator Parry wants the Senate to become more autonomous when it comes to finance, and not rely on executive government to approve travel. 

''I have a strong view about us becoming more financially independent,'' he said.

''I expressed this to people far and wide well before I became President.''

He said he was in discussions with Prime Minister Malcolm Turnbull about removing the five trips per year cap, and replace it with a capped budget of $250,000 instead.

Senator Parry told the committee there were overseas trips he would have liked to have gone on but couldn't due to the five trip allowance, such as the funeral of his counterpart in Canada.

''Currently, the Prime Minister, Speaker and I are in discussions about this, and the Prime Minister has sympathetic views towards this,'' he said.