More than 1,000 Afghan troops fled into neighbouring Tajikistan on Monday after clashes with the Taliban, who have made advances on the battlefield.
The departure of troops followed another weekend of fighting across much of the northern countryside, where the Taliban have overrun dozens of districts.
As Tajikistan rushed its own troops to "strengthen" the border, Moscow said it temporarily closed one of its consulates in Afghanistan's north as the security situation deteriorated.
The Afghan soldiers "did not want to surrender. They had asked for reinforcements but their call was ignored", said Abdul Basir, a soldier with a battalion in Badakhshan province, where troops fled across the border.
The US said on Friday that it had handed over Bagram Airbase, the centre of its operations, to Afghan security forces, effectively ending operations in the country after nearly two decades of fighting.
The move ended crucial US air cover for the Afghan army.
Tajikistan's national security committee said that 1,037 Afghan troops had fled into the country "to save their lives" after clashes with the Taliban during the night.
"Taking into account the principle of good neighbourliness and adhering to the position of non-interference in the internal affairs of Afghanistan, the military personnel of the Afghan government forces were allowed to enter Tajik territory," the committee told Tajikistan's state information agency.
Tajiki President Emomali Rakhmon has ordered "the mobilisation of 20,000 reserve troops to further strengthen the border between Tajikistan and Afghanistan", the presidency said later on Monday.
Afghan troops had already crossed into Tajikistan after earlier clashes in which the Taliban took control of a major border crossing.
The Afghan government has pledged to launch a counter-offensive in the north.
Hamdullah Mohib, the Afghan National Security Adviser, told Russia's RIA news agency that an operation was "absolutely" in the works.
On Monday, Russia said it had temporarily closed its consulate in the northern city of Mazar-i-Sharif, the capital of Balkh province and one of Afghanistan's largest urban centres, near the border with Uzbekistan.
"The situation is changing rapidly," Moscow's envoy to Afghanistan, Zamir Kabulov, told the state-run Tass news agency.
"The Afghan forces, as they say, have abandoned too many districts. This logically creates nervousness."
Mr Kabulov said many consulates in Mazar-i-Sharif had "temporarily suspended their activities until the situation becomes clear".
There were unverified reports that Iran and Turkey were among them.
But a spokesman at the Russian embassy in Kabul said Moscow had no intention of leaving the diplomatic mission.
"The embassy is well defended. Its evacuation is not planned," Nikita Ishchenko told RIA Novosti news agency.
Already thinly stretched with supply lines strained, Afghan security forces have been crumbling in the face of the Taliban onslaught.
Several bases and outposts were surrendered to the insurgents without a shot being fired.
"Afghan forces have lost their morale," said analyst Atta Noori in Kabul. "They are confused.
"In almost every district that the Taliban capture, they send a team of elders to talk to the soldiers and get them to surrender.
"It is an emergency situation for the Afghan government. They need to step up their counter-offensive as soon as possible."
The Taliban pressed on with their offensive across the north over the weekend, seizing most of Badakhshan and Takhar provinces, with government forces holding little more than the provincial capitals.
The speed and ease of the Taliban's effective takeover are a massive psychological blow to the Afghan government.
Both provinces had once served as the strongholds for the anti-Taliban Northern Alliance during the civil war in the 1990s and were never routed by the militants.
The dire situation in the north was accompanied by reports that the Taliban were also inching closer to the provincial capitals in their southern strongholds of Kandahar and Helmand.
Key districts on the outskirts of both cities have been taken by the group.
"We are so tired of this war," said Shir Mohammad Barekzai, a resident of Helmand's Nawa district, which was seized by the Taliban early on Monday.
Since May 1, when the US military began its final withdrawal of about 2,500 troops, Afghan soldiers and the Taliban have clashed fiercely across the countryside as peace talks in Doha stalled.
Despite the Taliban's rapid gains, the US has continued its withdrawal in accordance with President Joe Biden's decision to have all forces pull out by this year's 20th anniversary of the September 11 attacks.