Under the accord, the US is initially supposed to cut its troop presence from about 12,000 currently to 8,600 by mid-July, and close five of its roughly 20 bases across the country.
Troops have started leaving one base in Lashkar Gah, the capital of Helmand province in the south, and another base in Herat in the west, a US official told AFP on the condition of anonymity.
Even with the drawdown, US forces retain "all the military means and authorities to accomplish our objectives", Colonel Sonny Leggett, spokesman for US Forces-Afghanistan, said Monday, referring to American counterterrorism operations and support for Afghan forces.
Helmand, which along with neighbouring Kandahar province is considered a Taliban stronghold, is where US and British forces fought some of the bloodiest campaigns of the 18-year war.
Omar Zwak, spokesman for Helmand's governor, told AFP that "20 to 30" foreigners had left Lashkar Gah since the weekend. The initial drawdown comes as the Taliban, which see themselves as having achieved "victory" over America, test the Pentagon's resolve to protect local partners by conducting dozens of low-level attacks against Afghan forces. The US has only responded to a few of these attacks.
KABUL CHAOS Under the terms of the withdrawal deal, the Taliban are supposed to tackle jihadists such as the Islamic State group and Al-Qaeda, as well as hold talks with the Afghan government that were due to start Tuesday.
But Kabul is in disarray and appears unable to present a unified front to negotiate with the Taliban.
On Monday, President Ashraf Ghani was inaugurated for a second term following an election that was marred by fraud allegations while his rival, former chief executive Abdullah Abdullah, also declared himself winner and swore himself in as premier in a parallel ceremony.
Washington has denounced Abdullah's self-inauguration, urging unity in Kabul ahead of negotiations with the Taliban.
"Prioritising an inclusive government and unified Afghanistan is paramount for the future of the country and particularly for the cause of peace," Secretary of State Mike Pompeo said Monday.
Peace talks were supposed to start Tuesday but have been thrown into limbo by a dispute over the release of Taliban prisoners - something the insurgents have demanded as a prerequisite ahead of negotiations, but which Ghani has so far refused to do.
Ghani was expected later Tuesday to announce a decree on the issue and reveal details of the negotiating team.
A member of the Taliban's leadership council - the Quetta Shura - told AFP the insurgents had delivered a list of the 5,000 captives they wanted freed to the Afghan government.
But he accused Kabul of acting in bad faith, alleging that "the government (planned) to release only those prisoners who are elderly, very ill, or those whose sentences have expired".
The Taliban's political spokesman Suhail Shaheen tweeted Tuesday that any prisoners "handed over to us ... will be accepted (only) after verification by our delegation". "They should be the people whose names are in the list," Shaheen wrote.