"We've had some groups of Taliban, small groups, who have either started to come over or expressed an interest in talking", said Mattis.
Mattis said the goal was to take advantage of Taliban fracturing to peel off insurgents exhausted of fighting and create a process that could incorporate some Taliban leaders.
That reversed a trend of scheduled drawdowns under his predecessor, Barack Obama, and set the stage for an open-ended conflict.
The US has, in the past, also expressed hope of "peeling off" elements of the Taleban, and it was unclear how this new effort might be different.
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.
Trump has made no secret of anger toward Pakistan or his pessimism about Taliban peace talks, declaring on January 29 after a series of Taliban attacks in Afghanistan: "I don't see any talking taking place".
Two weeks ago, Afghan President Ashraf Ghani offered direct talks with the Taliban with no preconditions.
Mattis said he would be meeting with President Ashraf Ghani and top US commanders.
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Afghanistan experts have long anxious that a precipitous US exit could usher in defeat for the Afghan army.
"It has been a game changer because it has forced every actor to re-examine their assumptions", Ghani said.
However, Mattis says a diplomatic solution must be between Kabul and the Taliban.
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. Taliban so far have not responded to the offer.
The insurgent group has said it is prepared to negotiate, but only with the United States and not with the Kabul government.
"We do look toward a victory in Afghanistan", he said, adding, "Not a military victory - the victory will be a political reconciliation" with the Taliban. But he said it was still too much to expect the whole Taliban to do so. "But there are elements of the Taliban clearly interested in talking to the Afghan government", he said.
Last month, Ghani, hosting an worldwide conference in Kabul, offered the Taliban a ceasefire and political recognition to come to the peace table without preconditions. While he forecast that Afghan forces this year will continue to develop offensive combat power, he predicted the Taliban will "threaten Afghan stability, undermine public confidence by conducting intermittent high-profile attacks in urban areas", increase its influence in rural areas, and threaten district centers.
They have offered to talk directly to the United States about a possible peace agreement.
He also met NATO-led Resolute Support personnel and other top Afghan government officials to discuss the military effort and the potential for peace between the Taliban and the Afghan government, the U.S. Forces in Afghanistan said in its statement.