President Donald Trump's plan to end the stalemate in Afghanistan and eliminate the rising extremist threat involves sending up to 3,900 additional US forces, senior officials said.
The first deployments could take place within days.
In a national address on Monday night, Mr Trump reversed his past calls for a speedy exit and recommitted the US to the 16-year conflict, saying troops must "fight to win".
He warned against the mistakes made in Iraq, where an American military withdrawal led to a vacuum that the Islamic State group quickly filled.
Mr Trump would not confirm how many more service members he plans to send to Afghanistan, which may be the public's most pressing question about his strategy.
In interviews with television networks on Tuesday, vice president Mike Pence similarly would not give any clear answer. Instead, he cited Pentagon plans from June calling for 3,900 more troops.
"The troop levels are significant, and we'll listen to our military commanders about that," Mr Pence said. "And the president will make that decision in the days ahead."
US officials said there was no fixed number, but they said the Pentagon has told Mr Trump it needs that many fresh forces in addition to the roughly 8,400 Americans in the country to accomplish Mr Trump's objectives of "obliterating ISIS, crushing al Qaida, preventing the Taliban from taking over Afghanistan and stopping mass terror attacks against America before they emerge".
The 3,900 figure includes a combination of trainers, security forces and other support troops, according to the officials.
Defence secretary Jim Mattis also declined to confirm an exact number on Tuesday, saying he was waiting for more input from General Joseph Dunford, America's top military official.
Mr Mattis said he will "reorganise" some US troops in Afghanistan to reflect the new strategy.
The top US commander for the Middle East said he expects the first reinforcements to arrive "pretty quickly", within days or weeks.
"What's most important for us now is to get some capabilities in to have an impact on the current fighting season," Gen Joseph Votel, who spent last weekend in Afghanistan, told reporters travelling with him to Saudi Arabia on Tuesday.
Before he was a presidential candidate, Mr Trump ardently argued for a quick withdrawal from Afghanistan and called the war a massive waste of US "blood and treasure". On Monday, he suggested an open-ended commitment rather than a "time-based" approach.
"Conditions on the ground - not arbitrary timetables - will guide our strategy from now on," Mr Trump said.
At its peak involvement in 2010-2011, the US had roughly 100,000 troops in Afghanistan. President Barack Obama then started bringing them home, drawing criticism for the advance timetables he provided for his planned drawdown and ultimate withdrawal of forces.
Mr Trump was among those who argued that Mr Obama was aiding the enemy by telegraphing US intentions.
On Monday, Mr Trump said he would not discuss troop numbers, military tactics or timetables.
"America's enemies must never know our plans or believe they can wait us out," he said.
While such reticence may have a military rationale, the American public may insist that it has a right to know how many of its citizens are waging a war overseas in its name.
The administration invariably will have to provide updates to Congress, which pays the military's bills, and to key US allies, whose troop contributions it seeks, on the changing level of American manpower in Afghanistan.
Mr Obama reversed himself on withdrawing from Afghanistan as security worsened. Taliban militants have made gains across the country, and the fractious Afghan government currently controls about half the country.
Afghanistan's US-backed government welcomed Mr Trump's strategy, with President Ashraf Ghani saying it will help stabilise the region.
Allies responded positively, too.
Germany, which contributes 950 troops in northern Afghanistan, approved the US readiness for a "long-term commitment" and agreed the military's continued deployment should be "linked to the conditions on the ground".
Mr Trump offered few specifics of how his strategy would be implemented. He did not say how the US would get Pakistan to crack down on militant sanctuaries on its soil - long a point of contention that has led Washington to restrict aid to the country.
Insisting that the US was intent on "killing terrorists" rather than "nation building", Mr Trump gave little indication of how the US would use other instruments of American power to end the conflict.
Secretary of state Rex Tillerson said that after an effective military effort, a political settlement including some Taliban might be possible, echoing language of the Obama years. He said the US would support peace talks with the Taliban "without preconditions".