United Nations Secretary-General Antonio Guterres called on the Taliban to immediately halt their offensive and warned that Afghanistan is "spinning out of control".
He also said that "horrifying" reports have emerged that the Taliban have imposed severe restrictions on the rights of women and girls in the areas the militants have seized.
"I'm also deeply disturbed by early indications that the Taliban are imposing severe restrictions on human rights in the areas under their control, particularly targeting women and journalists," he told reporters.
"It is particularly horrifying and heartbreaking to see reports of the hard-won rights of Afghan girls and women being ripped away," Mr Guterres added.
The UN chief urged the Taliban: "This is the moment to halt the offensive. This is the moment to start serious negotiation. This is the moment to avoid a prolonged civil war, or the isolation of Afghanistan."
Taliban insurgents have tightened their grip on Afghanistan, seizing the second and third biggest cities and raising fears that an assault on the capital Kabul could be just days away.
A senior US defence official said there was concern that the Islamist group, in power from 1996-2001, could make a move on Kabul in days, but Washington was hoping the Afghan security forces would put up more resistance as the insurgents move closer to the capital.
NATO Secretary General Jens Stoltenberg has said the alliance would keep its civilian diplomatic presence in Afghanistan as it tries to support the Afghan government and security forces in the face of the Taliban's offensive.
"Our aim remains to support the Afghan government and security forces as much as possible. The security of our personnel is paramount. NATO will maintain our diplomatic presence in Kabul, and continue to adjust as necessary," Mr Stoltenberg said, in a statement following a meeting of NATO envoys.
The capture of Kandahar in the south and Herat in the west after days of clashes is a devastating setback for the government as the Taliban advances turn into a rout.
"The city looks like a front line, a ghost town," provincial council member Ghulam Habib Hashimi said by telephone from Herat, a city of about 600,000 people near the border with Iran. "Families have either left or are hiding in their homes."
Afghan First Vice President Amrullah Saleh said he was proud of the country's armed forces.
"It was decided with conviction and resolve that we stand firm against Taliban terrorists and do everything to strengthen the national resistance by all means and ways," he said on social media about a national security meeting chaired by President Ashraf Ghani. "We are proud of our (armed forces)."
A government official confirmed that Kandahar, the economic hub of the south, was under Taliban control as international forces complete their withdrawal after 20 years of war.
The fighting has also raised fears of a refugee crisis and a rollback of gains in human rights.
Some 400,000 civilians have been forced from their homes since the beginning of the year - 250,000 of them since May, a UN official said.
"NATO Allies are deeply concerned about the high levels of violence caused by the Taliban's offensive, including attacks on civilians, targeted killings, and reports of other serious human rights abuses," Mr Stoltenberg said.
"The Taliban need to understand that they will not be recognised by the international community if they take the country by force. We remain committed to supporting a political solution to the conflict," the statement said.
Under Taliban rule, women could not work, girls were not allowed to attend school and women had to cover their face and be accompanied by a male relative if they wanted to venture out of their homes. In early July, Taliban fighters ordered nine women to stop working in a bank.
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Of Afghanistan's major cities, the government still holds Mazar-i-Sharif in the north and Jalalabad, near the Pakistani border in the east, in addition to Kabul.
In response to the Taliban advances, the Pentagon said yesterday it would send about 3,000 extra troops within 48 hours to help evacuate US embassy staff.
Britain has said it would deploy about 600 troops to help its citizens leave while other embassies, including those of the Netherlands, Denmark, Norway and Germany, and aid groups said they were also getting their people out.
British Prime Minister Boris Johnson will hold an emergency response meeting to discuss Afghanistan, a spokesperson said.
The United Nations has said a Taliban offensive reaching Kabul would have a "catastrophic impact on civilians". But there is little hope for a negotiated end to the fighting, with the insurgents apparently set on a military victory.
Television footage showed families camping out in a Kabul park with little or no shelter, escaping violence elsewhere in the country.
The Taliban also took the towns of Lashkar Gah in the south and Qala-e-Naw in the northwest, security officers said. Firuz Koh, capital of central Ghor province, was handed over without a fight, officials said.
The militants, fighting to defeat the government and impose their strict version of Islamic rule, have taken control of 14 of Afghanistan's 34 provincial capitals since 6 August.
After seizing Herat, the insurgents detained veteran commander Ismail Khan, an official said, adding that they had promised not to harm him and other captured officials.
A Taliban spokesman confirmed that Khan, who had been leading fighters against the Taliban, was in their custody.
The speed of the offensive, as US-led foreign forces prepare to complete their withdrawal by the end of this month, has sparked recriminations over President Joe Biden's decision to withdraw US troops, 20 years after they ousted the Taliban following the 11 September attacks on the United States.
Mr Biden said this week he did not regret his decision, noting Washington has spent more than $1 trillion in America's longest war and lost thousands of troops.
The loss of Kandahar is a heavy blow to the government. It is the heartland of the Taliban - ethnic Pashtun fighters who emerged in 1994 amid the chaos of civil war.
US Secretary of State Antony Blinken and Defense Secretary Lloyd Austin spoke to Mr Ghani on Thursday and told him the United States remained "invested" in Afghanistan's security.
But at home, criticism of Biden's policy has been mounting.
The US Senate's Republican leader Mitch McConnell, said the exit strategy was sending the United States "hurtling toward an even worse sequel to the humiliating fall of Saigon in 1975", referring to North Vietnam's victory in the Vietnam war. He urged Mr Biden to commit to giving more support to Afghan forces.