The C.I.A. director, William J. Burns, traveled to Kabul for talks with the Taliban leadership, American officials familiar with his visit said on Tuesday, conducting the administration’s highest-level in-person talks so far with the new de facto leaders of Afghanistan.

Mr. Burns, a longtime former diplomat who is the Biden administration’s most experienced back-channel negotiator, met on Monday with Abdul Ghani Baradar, the Taliban leader who had led diplomatic negotiations in Qatar with the U.S. government that began during the Trump administration.

While American officials would not provide details of the brief trip, they said Mr. Burns was not there to negotiate an extension of President Biden’s planned Aug. 31 troop withdrawal. Indeed, after Mr. Burns departed, the Taliban announced they would reject any postponement of the American military’s departure, and Mr. Biden said he would not seek it, though he left open the possibility of shifting course.

Mr. Burns’ negotiations appeared to be more general, covering the evacuation operations and terrorist threats. American officials need the Taliban to tolerate the evacuation flights and to help stop the Islamic State or others from mounting attacks on Afghan civilians, including any suicide bombings outside the airport, American officials have said.

The Taliban consider the Islamic State’s Afghanistan branch a threat and the two have fought long battles in recent years. Islamic State leaders have criticized the Taliban leadership as overly moderate.

The Taliban have an incentive to cooperate. They want to secure international legitimacy and to try to avoid the isolation they experienced in the 1990s, when they were last in power. Taliban leaders have urged international governments to maintain their embassies in Afghanistan.

The United States sent thousands of troops to secure the airport, and the pace of evacuations has stepped up in recent days. But getting Afghans from their homes to the airport in Kabul safely has become more difficult and dangerous, and the Taliban said on Tuesday that they will no longer allow Afghans to leave.

Former officials have said that the United States will need more time, perhaps until late September, to try to ferry out Afghans who have applied for special visas from the United States.

The White House press secretary, Jen Psaki, declined to discuss Mr. Burns’ visit but noted the administration has acknowledged it is “in regular contact with the Taliban.” The C.I.A. and the National Security Council declined to comment on Mr. Burns’ trip, reported earlier by The Washington Post.

Mr. Burns, who titled his memoir “The Back Channel,” specialized in delicate, secret communications during his long State Department career. A former ambassador to Russia and Jordan who rose to the department’s No. 3 post during the Obama administration, he was responsible for the initial undisclosed discussions that ultimately led to the Iran nuclear talks in the Obama administration.

When Mr. Burns was chosen to run the C.I.A., officials in the incoming administration said he would act as a traditional intelligence chief assessing threats, not take on his old work as a diplomat. But the State Department tapped him as the Biden administration faces its gravest national security and foreign policy crisis.

Dispatching Mr. Burns also fit because with the fall of the Afghan government and the withdrawal of American diplomats and troops, the C.I.A. will bear much of the responsibility for monitoring Afghanistan going forward.

The visit was Mr. Burns’ second to Kabul this year. In April, as concerns mounted about the Afghan government’s ability to effectively fight the Taliban, Mr. Burns met there with Afghan intelligence officials.

While ultimate power in Afghanistan likely rests with the Taliban’s supreme leader, Haibatullah Akhundzada, Mr. Baradar has led negotiations with the West.

Mr. Baradar, a top Taliban leader since the group was formed, has a reputation as both a shrewd, battle-hardened military commander and a polished political operator and administrator. He has also long been seen as the Taliban leader least likely to take a hard line on either the group’s harsh moral code or its relations with the rest of the world.

Mr. Baradar, thought to have been born in 1968, is now the Taliban’s political leader, but even that description only hints at his stature. He fought the Soviets in the 1980s alongside Mohammed Omar, they were co-founders of the Taliban in 1994, and for 15 years he served as chief deputy to Mullah Omar, the Taliban leader.

While the Taliban were in power from 1996 to 2001, Mr. Baradar served as a provincial governor and deputy military chief. After they were ousted by the U.S.-led invasion in 2001 and the Taliban leadership took refuge in Pakistan, Western officials say, it was he, rather than the reclusive Mullah Omar, who mostly ran day-to-day operations, convening leadership and military councils, meeting with the Taliban’s shadow governors, overseeing finances and often directing ruthless insurgent operations in Afghanistan.

In 2009, Mr. Baradar reached out to the Afghan government to explore peace talks, but the Pakistani authorities arrested him in early 2010 and held him for more than eight years.

Pakistan was the Taliban’s chief sponsor and the Americans had long accused Pakistan of sheltering them, so the arrests of Mr. Baradar and other Taliban leaders came as a surprise. But it soon emerged that the Pakistanis, fearing a loss of influence in Afghanistan, wanted to sabotage prospects for a brokered end to the war.

With Mr. Baradar out of the picture, the nascent talks collapsed. Kai Eide, a former United Nations envoy to Afghanistan, later said, “I believe that he was already, before his arrest, the most prominent Taliban leader in favor of finding a political settlement.”

In his absence, other Taliban leaders rose to prominence and Mr. Baradar’s longtime ally and mentor, Mullah Omar, died.

In 2018, under pressure from the United States, Pakistan released Mr. Baradar and he quickly became the Taliban’s chief negotiator in talks with the United States held in Doha, Qatar.

When those talks produced the February 2020 agreement for American troops to withdraw, Mr. Baradar signed on behalf of the Taliban. A few days later, he spoke with Donald J. Trump — the first conversation between a U.S. president and a Taliban leader.