China is a responsible nation, and a constructor of and contributor to the current international system, the president said.
"We will continue to safeguard the international order and rules, and support free trade and the liberalization and facilitation of trade and investment," Xi said.
"The international community should abandon the cold-war mentality and advocate working together to build a community with a shared future for mankind," he said.
China wants to continue to strengthen cooperation with the IMF, Xi said.
He spoke positively of the IMF's important contribution to promoting global economic recovery and growth and maintaining financial stability, as well as its quota and governance reforms to increase the representation and say of developing and emerging market countries.
Xi also praised the IMF for caring about the development of China and Asia and for supporting the Belt and Road Initiative.
Lagarde spoke highly of the keynote speech delivered by Xi at the forum on Tuesday, particularly its positive messages on China's determined push for reform and opening up.
Xi's speech added certainty and hope to the world today, and the world needs leadership like China, she said.
Conservatism and unilateralism hurt the global economic and financial stability, Lagarde said, noting that the IMF's duty is to safeguard free trade and the multilateral system.
The IMF backs dialogue and cooperation, is committed to closer ties with China, and supports and actively participates in the Belt and Road Initiative, according to the managing director.