Mattis told reporters at the Pentagon he expected to sign an order sending the troops soon, but offered few details.
"The president has been very clear that we are not going to broadcast to the enemy how many [troops] are going [and] where exactly they are going," he said. "You know they are shifting to an even stronger train, advise, assist effort. I think that's plenty of transparency so that the American people know what we are doing, approximately how much of a troop commitment it is."
Mattis said about half of the new troops would be from the 82nd Airborne.
On Aug. 31, the secretary told reporters the reinforcements would advise and "enable the Afghan forces to fight more effectively" against the Taliban and other terror groups in the country.
The additional 3,000 troops would bring the total in country to about 14,000.
"We will not talk about numbers of troops or our plans for further military activities," Trump said in a speech at Fort Myer in Arlington, Va. "Conditions on the ground, not arbitrary timetables, will guide our strategy from now on. America's enemies must never know our plans or believe they can wait us out. I will not say when we are going to attack, but attack we will."
Trump, who ran for president on a platform that expressed skepticism of the United States' interventionist foreign policy, also said that being president changed his opinions on what would be the best strategy going forward.
"My original instinct was to pull out, and historically I like following my instincts," Trump said. "But all my life, I have heard that decisions are much different when you sit behind the desk in the Oval Office. In other words, when you are president of the United States."
Instead of pulling out, Trump said he now believes "the consequences of a rapid exit are both predictable and unacceptable" and that a "hasty withdrawal would create a vacuum that terrorists, including [the Islamic State] and al-Qaida, would instantly fill, just as happened before September 11."
On Aug. 30, the Pentagon acknowledged there are about 2,600 more U.S. troops in Afghanistan than they had publicly revealed over the past six months. Marine Lt. Gen. Kenneth McKenzie Jr. said there are about 11,000 troops in Afghanistan, not the 8,400 figure the Department of Defense previously gave.
U.S. troops in Afghanistan are on a two-fold mission amid the war in Afghanistan -- as part of a NATO-led operation to train and advise Afghan troops, and a counter-terrorism mission.