Parliament has rejected a move to restore Labor MP Harry Jenkins to his old job as Speaker while Peter Slipper waits for federal police to investigate claims he misused taxi dockets.

Mr Slipper again denied any wrongdoing but told Parliament yesterday his role would be filled by Deputy Speaker Anna Burke until the issues surrounding him were resolved.

He lamented that trial by media had become ''the order of the day'' and said he was entitled to have the matters brought against him dealt with by ''proper process''.

Mr Slipper, who quit the Liberal Party last year when he became Speaker, also faces a civil lawsuit, brought by his former adviser James Ashby, involving allegations of sexual harassment.

Manager of opposition business Christopher Pyne urged Parliament to restore confidence in Australia's democracy by reinstalling Mr Jenkins, who resigned last November 24.

The move to install Mr Jenkins as Speaker was tied 72-72. Ms Burke was not required to make a casting vote because a successful motion needed 76 votes.

Independent MPs Andrew Wilkie and Bob Katter voted with the opposition. AAP