This also includes ensuring that the government of Afghanistan continues to make the necessary reforms that its President Ashraf Ghani has already committed to and that he is moving out on.
Last month, Ghani, hosting an global conference in Kabul, offered the Taliban a ceasefire and political recognition to come to the peace table without preconditions.
US President Donald Trump's administration has also piled pressure on Pakistan to crack down on militant safe havens on its side of the Afghan-Pakistan border.
Mattis arrived in capital Kabul on an unaccounted visit - his third since taking charge a year ago - during which he met President Mohammad Ashraf Ghani.
"We've had some groups of Taliban, small groups, who have either started to come over or expressed an interest in talking", he added later.
NTSB Investigators Analyze Helicopter That Crashed Into East River
The flight originated from Helo Kearny Heliport in Kearny, New Jersey, not from the 6 East River Piers as previously reported. But an August 2009 collision over the Hudson River between a Liberty chopper and a small private plane killed nine people.
"All wars come to an end", Mattis said.
As part of the so-called South Asia Strategy, President Donald Trump previous year ordered the increased bombing of Taliban targets - including drug-making labs and training camps.
The group has insisted it would only negotiate with the United States, which it calls a "foreign occupying force". Taliban so far have not responded to the offer.
Over the past several months, the United States has ramped up assistance to the Afghan military by sending over thousands more troops to the country in its efforts to fight against the Taliban. Elements of the Taliban are open to talks with the Afghan government, Mattis said.
"We do look toward a victory in Afghanistan - not a military victory", he said.
Rohingya villages razed to make way for military bases
During the operations, Rohingya villages were burnt to the ground, while thousands were allegedly killed and women raped. He also said there are plans for police stations but not military installations.
An attack on a Kabul hotel killed more than 30 people in January and the attack on the streets of the Kabul later in the week claimed the lives of more than 100 people.
"We want the Afghans to lead and to provide the substance to the reconciliation effort", Mattis stated. The Taliban last week described the Afghan government as "illegitimate" and its peace process efforts as "deceptive", in a statement calling for a boycott of an Islamic scholars' conference in Jakarta.
Stephen Biddle, a George Washington University political science professor and longtime observer of the Afghan conflict, is skeptical that the new USA strategy will make a decisive difference militarily, although he sees "glimmers of hope" for progress toward a peace settlement.
While the United States has been stepping up battlefield pressure, Afghanistan's worldwide partners have sought to build diplomatic support from neighboring countries to push the militants to the negotiating table.
Mattis said the goal was to convince the Taliban that they could not win, which would hopefully push them towards reconciliation.
Reconciliation, Mattis said, was "almost an equal priority of my interest going in".
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Carrick revealed this at a press conference at Old Trafford on Monday while previewing the second-leg round of 16 UEFA Champions League clash against Sevilla .
More than 3,000 additional USA forces have also arrived in Afghanistan to boost the training and advising of local troops.