Liberals' Parry elected Senate president

Tasmanian Liberal Stephen Parry has been elected Senate president in a secret ballot on the first day of the new upper house.

Australian Greens' nominee Scott Ludlam won only the 10 votes of his own party, despite urging the crossbenchers to reject the deal for the presidency stitched up between Labor and the coalition.

Under the deal, Labor's Gavin Marshall will be elected deputy president later on Monday.

"We want to make the point that the crossbenchers are an important part of this chamber and it should not be an automatic assumption that either of the major parties should be handed either one of these positions," Senator Ludlam told parliament.

"It is the largest number of crossbenchers there's been in this place.

"And we believe that as part of the increasing diversity of this place, the crossbenchers should put themselves forward for positions such as this."

The final vote was Parry 63, Greens 10, with two informal votes and one senator absent.

Senator Parry said he would defend the Senate as being "truly independent" from the executive.

He replaces Labor's John Hogg in the role.