Mr. Holbrooke, who died in December 2010, had a turbulent relationship with Mr. Obama’s White House. But he assembled a team of experts from the Pentagon, the C.I.A., the Agriculture Department and other agencies to devise a civilian strategy for stabilizing Afghanistan that was designed to complement Mr. Obama’s military surge of 30,000 troops in 2009.

Among those on Mr. Holbrooke’s staff, in addition to Mr. Nasr, were Rina Amiri, an Afghan-born woman who advocated on behalf of women’s rights in her native country, and Barnett R. Rubin, a prominent scholar on Afghanistan and the Taliban at New York University.

Mr. Holbrooke also initiated contacts with the Taliban about negotiating a political settlement with the Afghan government, a process he said would have to involve neighboring Pakistan. Nine years later, many experts on Afghanistan say a settlement between Kabul and the Taliban remains one of the few options for bringing lasting peace to the country.

The special representative’s office “elevated the importance of the diplomatic and political equities to be on par with the military equities,” said Daniel F. Feldman, who served as Mr. Holbrooke’s deputy and later became the special representative himself. “What we’re still bereft of is any strategy for what’s going to lead to stability in Afghanistan.”

Mr. Trump’s decision to authorize the Pentagon to deploy more troops was a stopgap measure, driven by worries that the Taliban were making gains on the battlefield and that the government of President Ashraf Ghani of Afghanistan was in danger of falling. On Friday, a series of deadly bombings in Pakistan added to the sense of regional instability.

The White House National Security Council has met multiple times to work on a broader strategy. It is being labeled a “South Asia” policy, to distinguish it from the Obama administration’s so-called Af-Pak policy. Mr. Mattis has said he hopes to present the strategy by mid-July.

Mr. Tillerson and his chief of staff, Margaret Peterlin, attended at least one meeting last week, people briefed on the process said. But the State Department did not send an Afghanistan subject expert to the meeting, a practice that officials say has become commonplace under Mr. Tillerson.