deployed thousands more troops to Afghanistan as part of a “surge,” reaching nearly 100,000 by mid-2010. But the Taliban only grew stronger, inflicting heavy casualties on Afghan security forces despite American combat power and airstrikes.

killed Osama bin Laden in a compound in Abbottabad, Pakistan, where he had been living for years near a Pakistan military training academy. In June, Mr. Obama announced that he would start bringing American forces home and hand over responsibility for security to the Afghans by 2014.

By then, the Pentagon had concluded that the war could not be won militarily and that only a negotiated settlement could end the conflict — the third in three centuries involving a world power. Afghan fighters defeated the British army in the 19th century and the Russian military in the 20th century.

With the war at a stalemate, Mr. Obama ended major combat operations on Dec. 31, 2014, and transitioned to training and assisting Afghan security forces.

Nearly three years later, President Donald J. Trump said that although his first instinct had been to withdraw all troops, he would nonetheless continue to prosecute the war. He stressed that any troop withdrawal would be based on combat conditions, not predetermined timelines.

But the Trump administration also had been talking to the Taliban since 2018, leading to formal negotiations that excluded the Afghan government, led by President Ashraf Ghani.

an agreement with the Taliban that called for all American forces to leave Afghanistan by May 1, 2021. In return, the Taliban pledged to cut ties with terrorist groups such as Al Qaeda and the Islamic State affiliate in Afghanistan, reduce violence and negotiate with the American-backed Afghan government.

release 5,500 Taliban prisoners while receiving little in return, further alienating the Afghan government.

After the deal was signed, the Taliban stopped attacking American troops and refrained from major terrorist bombings in Afghan cities. The United States reduced air support for government forces, generally restricting them to instances in which Afghan troops were in danger of being overrun.

The primary objectives of the 2020 deal were for Afghan leaders and the Taliban to negotiate a political road map for a new government and constitution, reduce violence and ultimately forge a lasting cease-fire.

But the government accused the Taliban of assassinating Afghan government officials and security force members, civil society advocates, journalists and human rights workers — including several women shot in broad daylight.

Because of their strong battlefield position and the imminent U.S. troop withdrawal, the Taliban have maintained the upper hand in talks with the Afghan government, which began in September in Doha, Qatar, but have since stalled. The Pentagon has said the militants have not honored pledges to reduce violence or cut ties with terrorist groups.

After Mr. Biden announced in April the U.S. withdrawal of American forces, NATO said its 7,000 troops in Afghanistan would coordinate their withdrawal with the United States.

The Biden administration says it continues to support peace talks, but the Taliban appear in no hurry to negotiate. Nor have they explicitly said they would agree to a power-sharing government, implying instead that they intend to seek a monopoly on power.

impose tolls and taxes on truckers and motorists, providing official receipts valid anywhere in the country. The militants also have set up checkpoints on the outskirts of major cities, raising fears that they will attempt to wrest control of cities from the government after international forces depart.

The United States has spent at least $4 billion a year on the Afghan military — $74 billion since the start of the war. The Biden administration has pledged to continue supporting Afghan forces after American troops depart.

A classified intelligence assessment presented to the Biden administration this spring said Afghanistan could fall largely under Taliban control within two to three years after the departure of international forces.

And the Taliban have given no indication they will abandon their annual spring offensive, when they typically ratchet up combat operations with the arrival of warmer weather.

“The Taliban is confident it can achieve military victory,” the threat assessment concluded.

The report added: “The Taliban is likely to make gains on the battlefield, and the Afghan government will struggle to hold the Taliban at bay if the coalition withdraws support.”

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