U.S. Secretary of State Rex Tillerson has paid an unannounced visit to Afghanistan for talks with Afghan leaders on the new U.S. strategy to end the 16-year war.

The closed-door meeting took place on October 23 at Bagram Airfield north of Kabul, the United States' largest base in Afghanistan, as President Ashraf Ghani's Western-backed government is struggling to beat back insurgents in the wake of the exit of most NATO forces in 2014.

"Clearly we have to continue to fight against the Taliban, against others, in order for them to understand they will never win a military victory," Tillerson told reporters after the meeting with Ghani that was also attended by Afghan Chief Executive Abdullah Abdullah.

"It is imperative in the end that we are denying safe haven to any terrorist organizations or any extremists to any part of this world," he added.

The administration of President Donald Trump has recently unveiled a strategy to try to defeat the Taliban and other extremist groups in Afghanistan, and officials said more than 3,000 additional U.S. troops are being sent to the country to reinforce the 11,000 U.S. troops already stationed in the country.

Tillerson is on a six-day tour that also took him to Saudi Arabia and Qatar. He said he would visit Pakistan on October 24 to discuss U.S. requests for specific actions against extremist groups based there. He will then head to India.

"We have made some very specific requests of Pakistan in order for them to take action to undermine the support the Taliban receives and other terrorist organizations receive," Tillerson said.

Pakistan has denied that it harbors terrorists and says the United States is using Islamabad as a "scapegoat" for its own failure to win the war in Afghanistan.

In a statement, the U.S. Embassy in Kabul said Tillerson and Ghani "reaffirmed the U.S.-Afghan commitment to achieving peace, stability, and long-term prosperity in Afghanistan."

Tillerson said that the new U.S. strategy for South Asia "makes clear the United States' commitment to working with the government of Afghanistan and with partners across the region to achieve peace in Afghanistan and deny safe havens to terrorists who threaten that goal," it added.

The embassy statement said that Ghani "reiterated his support for the new U.S. strategy and emphasized his government's commitment to reforms."