American military commanders have argued during the monthslong policy assessment that the additional troops would enable the United States to reverse gains made by the Taliban and militant groups like the Islamic State’s Afghan affiliate, the Islamic State in Khorasan.
Administration aides, under orders to let Mr. Trump announce the details, hinted that any American commitment to increase force levels would require steps by the Afghans, like doing more to fight corruption.
Mr. Trump’s Monday evening speech will be his first nationally televised prime-time address since he spoke before Congress in January and follows a week of controversy over his reaction to the racially charged violence in Charlottesville, Va.
When it comes to Afghanistan, Mr. Trump entered office as the skeptic in chief, and any ramped-up engagement there poses political risks for the president, who rallied voters weary of war with his sharp criticisms of American involvement in the country.
“We should have a speedy withdrawal. Why should we keep wasting our money — rebuild the U.S.!” Mr. Trump tweeted about Afghanistan in January 2013, as he considered running for office in 2016.
The Afghanistan question has been the source of a long-running debate at the White House. Stephen K. Bannon, who was recently removed as a top Trump adviser, fought the military’s recommendation for more troops and backed a number of alternative options — including using private contractors instead of United States forces.
The decision on troops is just one component of a military and political plan for the region that Mr. Trump and his aides have been discussing for months, and it is politically important for the president to differentiate his approach from the Obama-era policies he sharply criticized.
Administration officials have been developing ways to try to pressure Pakistan to shut down the sanctuaries there for the Taliban, a goal Republican and Democrat administrations have pursued for years with little success.
A major concern is the Pakistan-based Haqqani network, which American intelligence agencies believe is responsible for some devastating attacks in and around Kabul. Funding for Pakistan, including contributions for Pakistani troops deployed near the border with Afghanistan, may be held up to more scrutiny than it is now, according to Pentagon and congressional officials.
Trump administration officials have also worked to lock in troop commitments from NATO and other Western nations, an important consideration for a president who has demanded that allies shoulder part of the burden.
Trump administration officials say they know they will need to reassure the American public that American military involvement in the nearly 16-year-old conflict will not be open-ended and will help combat international terrorism.
Moreover, many officials believe they need to do so without setting firm deadlines for reducing or withdrawing American troops, a practice President Obama embraced but which Trump officials assert denied the military needed flexibility and played into the hands of the United States’ adversaries.
One way to address that concern, administration officials have said in recent weeks, might be to stipulate that the Afghans would need to satisfy certain conditions, like fighting corruption or improving governance, to continue to receive American economic and military support.
A number of high-level participants in the review have important experience on these issues, especially Lt. Gen. H. R. McMaster, Mr. Trump’s national security adviser, and Maj. Gen. Ricky Waddell, the deputy national security adviser. Each headed an anti-corruption task force in Afghanistan.
Few people think that the war in Afghanistan can be ended anytime soon.
Gen. John W. Nicholson, commander of the American-led international force in Afghanistan, told Congress in February that the United States and its NATO allies were facing a “stalemate.”
According to a report to Congress by the Special Inspector General for Afghanistan Reconstruction, 57 percent of the districts in the country were under the Afghan government’s control as of November 2016, a 15 percent decrease from the previous year.
An estimated 8,400 American troops are stationed in Afghanistan, most assigned to an approximately 13,000-strong international force that is training and advising the Afghan military. About 2,000 American troops are tasked with carrying out counterterrorism missions along with Afghan forces against militant groups like the Islamic State’s affiliate.
Several hard-line lawmakers, including Senator John McCain, the Arizona Republican who is chairman of the Senate Armed Services Committee, had complained that Mr. Trump was delaying his decision as security in Afghanistan was eroding. Earlier this month, Senator McCain announced he had drafted an amendment outlining a new Afghan strategy because Mr. Trump had taken so long to act.
As recently as Monday, Mr. Mattis said that administration was weighing some radically different approaches, including withdrawing American forces and sending contractors to fight in Afghanistan rather than troops. The cost of deploying troops and contributions of allies were among the president’s questions.
“There were several options,” Mr. Mattis said. “The reason we had to get back together was he kept asking questions on all of them.”