Taliban officials on Friday said the group controlled most of Afghanistan's territory and promised not to attack provincial capitals or seize them by force, airing hopes for a "political resolution" for escalating tensions in the north of the country.
A delegation of the Taliban visited Moscow this week to offer assurances that their quick gains on the ground in Afghanistan do not threaten Russia or its allies in Central Asia.
Earlier this week, Taliban advances forced hundreds of Afghan soldiers to flee across the border into Tajikistan, which hosts a Russian military base.
Tajikistan in turn called up 20,000 military reservists to strengthen its southern border with Afghanistan.
Russian officials have expressed concern that the Taliban surge could destabilize the ex-Soviet Central Asian nations north of Afghanistan.
At a press conference in the Russian capital on Friday, Taliban officials vowed they would "not allow anyone, any individual, any entity to use the soil of Afghanistan" against other countries, including the United States and its allies.
Taliban negotiator Shahabuddin Delawar said that the group controlled 85% of territory in Afghanistan.
The Taliban also aired their willingness to find a peaceful resolution of the conflict.
Spokesman Mohammad Sohail Shaheen said they didn't want to fight and wanted to find a political resolution through negotiations in Qatari capital Doha.
Delawar also assured that the group will not be attacking and forcefully seizing provincial capitals.
The guarantees not to do that, he added, were brought to the Afghan authorities together with demands to implement agreements on the release of prisoners.
The Taliban have swept through dozens of districts in recent weeks taking control, often without a fight.
While they have yet to take a provincial capital there were reports they entered the capital of northern Badghis province and there was fighting in the area.
The Taliban claim to control about one third of Afghanistan's 421 districts and district centers.
They control several key border crossings with Iran, Uzbekistan and Tajikistan.
On Friday Iranian media said the Taliban were in control of two border crossings between Afghanistan and Iran, the most significant being Islam Qala which Taliban said Thursday they now controlled.
Iranian State Radio said that 300 Afghan soldiers and civilians had slipped across the border to Iran.
Last weekend more than 1,000 Afghan army soldiers crossed over to Tajikistan after Taliban swept through most districts in the northeastern province of Badakhshan.
Northern and western Afghanistan are the traditional strongholds of the U.S.-allied warlords.
In the south and east of Afghanistan, the former heartland of the Taliban, several districts have fallen to the group and many more have long been in their control.