Hollywood veteran Eastwood, an outspoken conservative, gave a speech on Thursday evening (August 30) in which he "debated" with an empty chair representing Obama.
The incumbent US president's campaign team posted a photograph on his official Twitter page with the caption: "This seat's taken."
Republican presidential nominee Mitt Romney's campaign team distanced themselves from the content of Eastwood's speech on Thursday night (August 30), saying: "Judging an American icon like Clint Eastwood through a typical political lens doesn't work.
"His ad-libbing was a break from the political speech-making, and the crowd enjoyed it."
The US presidential election takes place on Tuesday, November 6.