The refugees, including children, have escaped as the militia takes control of vast areas in Afghanistan.
Tajikistan has said that almost 350 refugees from Afghanistan had crossed into the Central Asian country, fleeing sweeping gains by Taliban fighters as foreign forces withdraw.
Border guards in the ex-Soviet country said on Wednesday those fleeing included 177 minors, and that two babies had died during the journey to the mountainous and impoverished country.
The Taliban's offensive has seen a stream of Afghans make their way across the border. Earlier this months more than 1,000 government troops fled to Tajikistan after the fighters seized a border crossing between the countries.
READ MORE: Tajikistan seeks help from Russian-led bloc
The militia in recent weeks has brought huge swathes of Afghanistan under its control as foreign troops withdraw, including the country's main Shir Khan Bandar border crossing with Tajikistan.
The border guards said the refugees, who included some 64 boys and 113 girls, crossed from the Badakhshan province, brining with them herds of livestock.
Tajikistan has even considered setting up camps for Afghan refugees, Reuters reported earlier this month.
Taliban now control or at least have driven Afghan govt security forces from three major and multiple minor border crossings (from Kunduz into Tajikistan; from Herat into Iran (and Turkmenistan); now Kandahar into Pakistan).— Andrew Watkins (@and_huh_what) July 14, 2021
Now clearly a trend & likely a strategic approach. https://t.co/xwtY98n0rz
Moscow, an important power broker in the region was closely watching the offensive, concerned about the security of countries in ex-Soviet Central Asia where it maintains military bases.
On Wednesday, about 1,000 troops at Russia's 201st military base in Tajikistan's capital Dushanbe took part in drills, Russian news agency Interfax reported.
The agency cited a statement by Russia's Central Military District as saying the exercises were meant for unit commanders and combat chiefs to ready for "combat operations in a dynamically changing situation".
The 201st base is one of Russia's most important foreign bases and has the aim of helping maintain stability in Central Asia and providing support for Tajik troops.
Set up in 2005 and made up of three separate installations, the base houses about 5,500 troops.
In 2012, Tajikistan gave Russia an extension on the base through 2042 so it could help police its border with Afghanistan.
Tajikistan is a member of the Moscow-led Collective Security Treaty Organization (CSTO) and the Shanghai Cooperation Organisation (SCO), which includes Russia.
Moscow expects the Taliban to fulfil its pledge not to threaten Russia or its allies in Central Asia, the Kremlin envoy on Afghanistan said in an interview published earlier on Wednesday.
Zamir Kabulov, who met with a Taliban delegation that visited Moscow last week, voiced confidence that the Taliban would focus on securing their gains in Afghanistan and wouldn't try to challenge the countries of the region.
"They visited Moscow to offer guarantees on behalf of the Taliban's supreme leadership that the territory of Afghanistan will not be used against the interests of third countries,” Kabulov said in an interview with the state RIA-Novosti news agency.
The Dushanbe meeting
Foreign ministers of SCO countries met in Dushanbe on Wednesday and issued a joint statement expressing their "deep concern over the growing tension in the northern provinces of Afghanistan".
"We urge all parties involved in the conflict in Afghanistan to refrain from using force and actions that could lead to destabilisation and unpredictable consequences in the areas of Afghanistan's borders with the SCO member states," the statement said.