The two leaders had a one-on-one meeting, followed by expanded talks attended by her majesty Queen Rania and HRH Crown Prince Hussein.
In the meeting, the leaders also reviewed the latest regional and international developments, including the Palestinian issue, the situation in Syria and Iraq, and the war on terrorism.
Both sides affirmed their commitment to continuing co-ordination and co-operation on issues of mutual concern, to advance relations and bolster global peace and security.
The Royal Hashemite Court's official website reported the king thanked Governor-General Cosgrove for the hospitality shown during the state visit to Australia last year, and his majesty said the two countries have always had a warm relationship and strong political, military and security ties.
The king also expressed commitment to working towards strengthening economic ties with Australia.
Jordan and Australia face common challenges, his majesty said, noting that the Governor-General’s visit is a reminder of the special relationship shared by the two countries and their peoples.
Recalling their majesties’ visit to Australia last year, Governor-General Cosgrove voiced hope that his visit to Jordan will be a further demonstration of the friendship between the two countries that will continue to prosper in the future.
Discussions covered efforts to push the peace process forward and relaunch serious and effective negotiations between the Palestinians and the Israelis to resolve the conflict and secure just and comprehensive peace.
Talks addressed the burden carried by Jordan due to the Syrian refugee crisis, with the king thanking Australia for its support to mitigate the impact of this burden and enable the Kingdom to continue to provide humanitarian and relief services to the refugees.