Morgan spent more than 30 years in politics, including near ten years as First Minister between 2000 and 2009 when he created the Faith Communities Forum.
In a statement announcing its "great sadness" at his death, the Church in Wales said: "We are particularly grateful for his commitment to interfaith relations.
"He set up the Faith Communities Forum in response to 9/11 and that has been pivotal in nurturing today's strong relationships both between Wales' diverse faiths and between those faiths and the Welsh Government.
Political parties in Wales have suspended campaigning on Thursday as a mark of respect for Rhodri Morgan, who made a new for himself on the political scene when he became MP for Cardiff West in 1987.
Honouring his predecessor, former Mr Jones said: "He was funny, clever, engaging on almost any topic and absolutely passionate about all things Welsh.
"I owe him a great deal; just as we all do in Wales. He did so much to fight for, and then establish devolution in the hearts and minds of the public in our country."
Andrew RT Davies, leader of the Welsh Conservatives said: "As first minister, his answers in the chamber were always worthy of attention and his encyclopaedic knowledge across his brief ensured he was rarely wrong-footed.
Plaid Cymru said: "We are suspending election campaigning for the day as a mark of respect to the former FM of Wales Rhodri Morgan who passed away yesterday."