At the top of a meeting with Mattis on Tuesday, Afghan President Ashraf Ghani called the new strategy a "game-changer".
However, the insurgents, who seized a district center in western Afghanistan earlier this week, have given no public sign of accepting Ghani's offer, instead issuing several statements suggesting they meant to keep fighting. But Talibans state the sending of soldiers by the U.S. to Afghanistan shows that Washington does not really want the peace.
But the Taliban has so far ruled out direct talks with the Western-backed government, which they say is illegitimate.
Mattis said he's seen initial indications that there have been changes in Pakistan's behavior but that he wants to use the trip to find out more.
The military is battling a Taliban insurgency while also fighting Daesh terrorist group's gradual expansion in the country's north and its regular attacks in the capital Kabul.
They have offered to talk directly to the United States about a possible peace agreement.
The visit is Mattis's second since President Trump announced last August that, despite his instinct to pull US troops out of Afghanistan, his administration would take a more aggressive approach to the conflict, now in its 17th year.
Mattis, though, said that "right now, we want to go by, with and through the Afghan-led process".
Reconciliation, Mattis said, was "almost an equal priority of my interest going in".
Ghani hailed the new U.S. strategy for South Asia that allowed American soldiers more authority and resources to target militants in Afghanistan without any time restrictions unlike the previous administration under former U.S. President Barack Obama.
These and other moves boosted the number of U.S. troops in Afghanistan by at least 3,500 to a total of more than 14,000.
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