"It may not be that the whole Taliban comes over in one fell swoop, that would be a bridge too far, but there are elements of the Taliban clearly interested in talking to the Afghan government", he told reporters aboard a military jet.
Mattis said the goal was to convince the Taliban insurgents that they could not win, which would hopefully push them towards reconciliation.
On February 28, Afghan President Ghani offered to allow the Taliban to establish itself as a political party and said he would work to remove sanctions on the militant group, among other incentives, if it joined the government in peace negotiations.
The Afghan government and the Taliban held peace talks in 2015, but they broke down nearly immediately.
"The Anardara district headquarters is under the insurgents' control and right now, an intense battle is going on all around the district center and government offices", said Bakhtawer.
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The visit comes as the U.S. injects new resources into the stalemated war.
"We do look toward a victory in Afghanistan", he said.
"It's all working to achieve a political reconciliation, not a military victory", Mattis said.
More than 3,000 additional U.S. forces have also arrived in Afghanistan to boost the training and advising of local troops.
The defence secretary, who commanded USA troops as a Marine general in southern Afghanistan during the war with the Taliban in 2001, said that getting the militants on board for reconciliation may be a bridge too far.
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They have offered to talk directly to the United States about a possible peace agreement.
Mattis said some of his indications, which he did not detail, dated back before Ghani's remarks. While the United States military says the strategy has hit the Taliban hard, they still control or contest much of the country.
This is Mattis's second visit to the war-torn country after he last visited in September.
U.S. 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 also said he had seen some changes in Pakistan's behaviour since Trump blasted the country past year for harbouring the Taliban.
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Indications that he was in good touch came in the second game of the match when he sealed a break to go 2-0 ahead. He then took Federer to deuce in the next game. "I haven't really checked out my draw entirely", he said.