The Dirty Harry actor came under scrutiny after what some critics described as a "bizarre" address, during which he debated with an empty chair as a stand-in for Obama.
After the speech, the US president's campaign team tweeted a photograph of Obama in his official chair with the caption "This seat's taken".
Obama has now responded to Eastwood's speech in an interview with USA Today, asserting that he is still a fan of the veteran actor and director.
"I am a huge Clint Eastwood fan," Obama revealed. "He is a great actor, and an even better director. I think the last few movies that he's made have been terrific."
In regards to the speech itself, he added: "One thing about being president or running for president - if you're easily offended, you should probably choose another profession."
The Democratic National Convention is set to kick off this Tuesday (September 4) in Charlotte, North Carolina.
Watch a video of Clint Eastwood's speech below: