"The two heads of state discussed the development of the countries' relationship and other issues of their common interest such as the North Korean nuclear issue, and agreed to cooperate in overcoming the spread of trade protectionism," it said in a press release.

Their 20-minute conversation came as Turnbull wished to congratulate Moon on his recent election as Seoul's new leader.

Moon came into office on Wednesday following his landslide victory in a rare presidential by-election the day before.

The new South Korean president noted the countries' bilateral trade has been growing since they implemented their bilateral free trade agreement (FTA) in December 2014, and expressed hope the countries will further expand their trade relations.

Moon and Turnbull have also agreed to enhance their countries'

cooperation on ending North Korea's nuclear ambition, agreeing to hold a two-on-two meeting involving their foreign and defense ministers.

They invited each other to their countries while expressing hopes to meet in person at the upcoming G20 meeting slated to be held in Germany in July. (Yonhap)