The cost of firebrand former Labor leader Mark Latham's homophobic tweet about a political rival has more than tripled and is set to cost more than half a million dollars.

Independent NSW MP Alex Greenwich was awarded $140,000 in damages in September after he successfully sued the former federal opposition leader.

Mr Latham rejected a settlement offer a month after the tweet was posted, the Federal Court was told.

The offer involved a retraction of the comments, $20,000 in compensation and an apology that Mr Greenwich's barrister said was not 'grovelling or humiliating' or requiring an admission the comments were defamatory.

Instead, they recognised it caused distress, Matt Collins KC said.

It was posted at the time of the 2023 state election in response to a post that quoted Mr Greenwich describing Mr Latham as a 'disgusting human being'.

Mr Latham's lawyer argued the former One Nation MP should only have to pay a quarter of his rival's costs because it was not unreasonable for him to refuse the settlement offer.

He noted an apology to a political rival 'could be used against' Mr Latham for the rest of his career, and stressed the difficulty of complying with the requirement to disable and monitor commentary on his apology.

Justice David O'Callaghan agreed it was not unreasonable for Mr Latham to reject the offer, finding the undertakings sought were 'very broad and unlimited in time'.