Australian Prime Minister Scott Morrison says tensions between his country and Turkey have eased after conciliatory comments from President Recep Tayyip Erdogan's office on Wednesday.

A diplomatic row flared in the wake of Friday's gun massacre at two mosques in New Zealand, when Erdogan warned Australians and New Zealanders going to Turkey with anti-Muslim views would return home in coffins, like their ancestors who fought at Gallipoli in World War I.

Morrison slammed the comments as "highly offensive," but on Wednesday a spokesman for Erdogan said the president's words were "taken out of context," saying he'd framed them "in a historical context" since he was speaking near commemorative sites near the Gallipoli.

Morrison told reporters Thursday progress had been made over the row after a "moderation of the president's views."