WASHINGTON — In one of the Islamic State’s first responses to President Obama’s declaration that he would “degrade and ultimately destroy” it, the group released a short video late Tuesday in which it appeared to say that its militants would kill American ground forces should President Obama deploy them.

The timing of the video’s release was curious. Just hours earlier, President Obama’s top military adviser had told Congress that he would recommend calling out American troops against the Islamic State if the current airstrike campaign was not sufficient — even though Mr. Obama has ruled out that option.

The clip is only 52 seconds long and is billed as a preview for a longer video. With slow-motion replay, quick edits and high-quality video images, it looks like a Hollywood trailer.

It begins with American tanks and troops under attack by fire and American soldiers carrying a wounded comrade into an armored vehicle. The images flick by, including a shot of the “Mission Accomplished” banner that served as a backdrop on the day President George W. Bush landed on an aircraft carrier six weeks after the United States invaded Iraq in 2003. That is followed by shots of Mr. Obama and the White House at night.