Mr. Obama says the U.S. will pull out 10,000 troops by the end of this year, with a total of 33,000 brought home by next summer.
There are currently 100,000 U.S. troops in Afghanistan, and there have been demands in Congress and elsewhere for a bigger pullout.
Congressman John Yarmuth of Louisville was among those hoping for a larger immediate drawdown.
Yarmuth, a Democrat, has criticized the war in Afghanistan as lacking a clearly-defined mission and metrics for measuring success.
He and dozens of other House lawmakers from both parties sent a letter to the president Tuesday, urging him to begin a “significant and sizable” troop reduction in Afghanistan.
(Information for this story also came from the Associated Press)