Its authenticity could not immediately be confirmed. While the video does closely resemble others released by the Islamic State, it lacked the theatrics and high-quality editing that other videos have had.
The 11-minute video begins with a selection of news clips showing the aftermath of the attacks, with French President François Hollande condemning them.
Later in the video, a man identified as "Al Karar the Iraqi" speaks to the camera, threatening the "crusader" nations in the coalition against the Islamic State. The U.S. capital is specifically singled out.
"We say to the states that take part in the crusader campaign that, by God, you will have a day, God willing, like France's and by God, as we struck France in the center of its abode in Paris, then we swear that we will strike America at its center in Washington," the man says, according to a translation from Reuters.
A different man, identified as "Al Ghareeb the Algerian," also said that European nations should expect similar attacks.
"I say to the European countries that we are coming — coming with booby traps and explosives, coming with explosive belts and [gun] silencers and you will be unable to stop us because today we are much stronger than before," he said.
Friday's attacks in Paris, which have left at least 132 people dead, were claimed by the Islamic State shortly afterward. French warplanes launched a retaliatory attack on Sunday, dropping 20 bombs on the Islamic State's de facto capital in Raqqa, Syria.
As reported by The Washington Post's Metro section, the FBI's Washington Field Office declined to comment about the purported video threat on Monday, but did refer to a statement it released in the wake of the Paris attacks on Friday.
"The Department of Homeland Security and the Federal Bureau of Investigation are closely monitoring the unfolding events in Paris and we remain in contact with our counterparts in the region," the statement said. "At this time, there is no specific or credible threat to the United States. We will not hesitate to adjust our security posture, as appropriate, to protect the American people."
Hugh Naylor in Beirut contributed to this post.
This post has been updated.