Saturday was the 25th anniversary of the withdrawal of Soviet forces, Khaama Press reported.
"The Islamic Emirate of Afghanistan is calling on its people to deal with today's invaders the same they did with the yesterday's invaders," Taliban spokesman Qari Yousuf Ahmadi said in a statement.
"We want to remind the Americans that we did not accept invaders with their sweet and nice slogans in the past," he added. "We eliminated them from the world map. God willing, your destiny will be the same."
The Soviet Union invaded Afghanistan Dec. 25, 1979, and installed a communist government, which collapsed after the last Soviet troops withdrew on Feb. 15, 1989. The resulting civil war eventually led to the Taliban taking control of the country.
More than 14,000 Soviet troops were killed and 50,000 wounded during the occupation.