"God instituted marriage. And for the president to now back something that is against God's position and – is a big problem for him with not only Evangelical churches, but African-American churches across this country who are very conservative," said Graham.
When pressed by Morgan about how he felt about homosexuals, Graham stressed that his position on marriage was not an issue of gay rights but rather based on what God had created.
"Listen, I cannot accept gay marriage. I'm not homophobic. I'm not against gay or lesbian people. They are free to live however they want to live," said Graham.
"But I believe God makes it very clear that marriage is between a man and a woman…There's no discussion about it. And for me to support any other definition other than God's definition would be wrong."
This is not the first time Graham has been critical of Obama's statements regarding the president's changing position on the marriage definition.
Back in May, Graham released a statement in response to the president's announcement, declaring that Obama had "shaken his fist at the same God who had created and defined marriage."
"It grieves me that our president would now affirm same-sex marriage, though I believe it grieves God even more," said Graham in May.
The Rev. Franklin Graham's remarks on CNN come a few days after his father, the Rev. Billy Graham, met with Republican candidate Mitt Romney.
Last Thursday, Romney visited Billy Graham at his home in Montreat, N.C. Billy Graham released a statement speaking well of the meeting.
"It was an honor to meet and host Gov. Romney in my home today, especially since I knew his late father former Michigan Gov. George Romney, whom I considered a friend," said Billy Graham.
"I hope millions of Americans will join me in praying for our nation and to vote for candidates who will support the biblical definition of marriage, protect the sanctity of life and defend our religious freedoms."
Not long after the meeting, the Billy Graham Evangelistic Association removed Mormonism from the list of cults on its website. In an interview with the North Carolina publication The Citizen Times, Ken Barun, a spokesman for the BGEA, explained that it was removed "because we do not wish to participate in a theological debate about something that has become politicized during this campaign."