"There is interest that we've picked up from the Taliban side", Mattis told reporters shortly before landing in Kabul on Tuesday, saying the signs date back several months.
Conference participants will call for an urgent start of direct talks between the Kabul government and the Taliban, the press office of Uzbekistan´s foreign ministry said in a written reply to questions from Reuters.
Mattis makes surprise Kabul visit
Mattis planned to meet with Gen. John Nicholson, the top American commander in Afghanistan, as well as Afghan President Ashraf Ghani.
In return, the militants would have to recognize the Kabul government and respect the rule of law.
The Taliban overran a district headquarters in Afghanistan's western Farah province early on Monday, killing and wounding at least 15 members of the security forces, a provincial official said. The former Marine general said it "may be a bridge too far" to expect the Islamic insurgent force to sit down at the negotiating table "in one fell swoop".
The insurgent group has said it was prepared to negotiate, but only with the United States and not with the Kabul government.
"Right now the district headquarters and the area around it are under control of the Afghan security forces", Rahimi said, adding that "fighting is ongoing in three different parts of the district" as Afghan forces pursue the Taliban.
Mattis said the ultimate victory in Afghanistan will be a "political reconciliation" between Kabul and the Taliban, with a country capable of handling its own security. The group ruled Afghanistan until 2001 when it was defeated by a USA -led troops in the wake of the September 11 attacks and it is fighting to restore Islamic rule in the country. "Not a military victory - the victory will be a political reconciliation".
Ghani's offer of peace talks comes as civilian casualties have soared in recent months, with the Taliban increasingly targeting towns and cities in response to Trump's new and more aggressive military policy.