"The US has made clear ... (its) support (for) a sovereign unified Afghanistan, a democratic Afghanistan, of charting a path to peace, prosperity and self-reliance," Tillerson told reporters. "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."
After a failed rocket attack on US Defense Secretary James Mattis at Kabul's Hamid Karzai International Airport last month, Tillerson flew directly into Bagram Air Base for his first official visit to the country. Tillerson spent three hours in a heavily-guarded building on the base.
The US military facility has also been a frequent target of mortars and explosive-laden vehicles, but has escaped attacks in recent months despite a spike in attacks in the country by the resurgent Taliban.
The militant group has stepped up attacks as a direct challenge to US power. More than 200 people have been killed in multiple attacks on security installations and mosques across the country in the past week.
A spokesman for the Taliban told Agence France-Presse news agency last week the attacks were "a clear message ... the enemy who thought they had scared us with the new Trump strategy have now been given a lesson."
Tillerson will visit Pakistan on Tuesday and India on Wednesday. In Pakistan he is expected to press Prime Minister Shahid Khaqan Abbasi and Foreign Minister Khawaja Asif to crack down on militancy in the country.
President Trump has threatened to cut aid and impose sanctions on Pakistan for allegedly harboring militants and supporting the Afghan Taliban and the Haqqani network.
In India he is expected to request that the government expands its economic and development assistance to Afghanistan.