It was "a positive step towards the implementation of (the) Doha agreement," a spokesman for the Islamist group, Mohammad Naeem, said in a statement.
Trump said on Twitter on Wednesday: "We should have the small remaining number of our BRAVE Men and Women serving in Afghanistan home by Christmas!"
It was unclear from his Tweet whether Trump was giving an order or verbalizing a long-held aspiration.
The Doha agreement, a landmark deal signed between the U.S. and Taliban in February, drew up plans to pull out foreign forces from Afghanistan after two decades of war.
In exchange, the insurgent group promised security guarantees including negotiating a permanent ceasefire and a power-sharing formula with the Afghan government.
Trump's announcement came just hours after national security adviser Robert O'Brien said the U.S. had less than 5,000 troops in Afghanistan currently and would go down to 2,500 by early next year.
"Ultimately, the Afghans themselves are going to have to work out an accord, a peace agreement. ... It's going to be slow progress, it’s going to be hard progress, but we think it’s a necessary step — we think Americans need to come home," O'Brien told an event at the University of Nevada, Las Vegas on Wednesday.
Trump, in the midst of a reelection campaign, has made walking away from "ridiculous endless wars" the cornerstone of his foreign policy, even though thousands of troops remain in Iraq, Syria and Afghanistan.
The White House's plan for the drawdown will almost certainly be subject to review should Trump lose his bid for a second term in the Nov. 3 election.
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Trump's comments could, however, further weaken the Afghan government's leverage during negotiations with the Taliban. While the talks have been taking place in Qatar's capital, Doha, scores of Afghan soldiers and Taliban fighters have been killed in clashes. Dozens of civilians have also died in recent weeks.
About 2,400 U.S. service members have been killed in the Afghan conflict and many thousands more wounded.
Wednesday marked 19 years since the United States invaded Afghanistan to topple the Taliban rulers who had harbored al Qaeda militants that attacked the United States on Sept. 11, 2001.