Gunshots were heard around the presidential palace in Afghanistan's capital Kabul early Sunday as the Taliban entered the city, the Interior Ministry said in a statement. Meanwhile, Pakistan's Interior Minister Sheikh Rashid Ahmed said that the group had taken the Torkham border crossing, the last post still under Afghan government control. The Taliban now holds all of Afghanistan's border crossings amid their offensive across the country.

Ahmed also told local broadcaster Geo TV that Pakistan halted cross-border traffic there because of it.

Helicopters are landing at the U.S. Embassy in Kabul as diplomatic vehicles leave the compound amid the Taliban advance on the Afghan capital.

The rapid shuttle runs by helicopters came Sunday as wisps of smoke rose from the embassy’s roof. U.S. officials previously said that diplomats inside had begun destroying sensitive documents.

The moves came as the Taliban earlier seized the last major city outside of Kabul held by the country’s increasingly isolated central government, cutting off the capital to the east and tightening their grip on the nation as tens of thousands fled their rapid advance.

The collapse of Jalalabad, near a major border crossing with Pakistan, leaves Afghanistan's central government in control of just Kabul and six other provincial capitals out of the country's 34. In a nationwide offensive that has taken just over a week, the Taliban has defeated, co-opted or sent Afghan security forces fleeing from wide swathes of the country, even with some air support by the U.S. military.

The rapid shuttle-run flights near the embassy began a few hours later as diplomatic armored SUVs could be seen leaving the area around the post. The U.S. government did not immediately acknowledge the movements. However, wisps of smoke could be seen near the embassy's roof as diplomats urgently destroyed sensitive documents, according to two American military officials who spoke on condition of anonymity because they were not authorized to discuss the situation.

The Czech Republic also approved a plan to begin withdrawing their Afghan staff from their embassy after earlier taking their diplomats to Kabul Hamid Karzai International Airport.

President Ashraf Ghani, who spoke to the nation Saturday for the first time since the offensive began, appears increasingly isolated as well. Warlords he negotiated with just days earlier have surrendered to the Taliban or fled, leaving Ghani without a military option. Ongoing negotiations in Qatar, the site of a Taliban office, also have failed to stop the insurgents' advance.

Thousands of civilians now live in parks and open spaces in Kabul itself, fearing the future. While Kabul appeared calm Sunday, some ATMs stopped distributing cash as hundreds gathered in front of private banks, trying to withdraw their life savings.

Militants posted photos online early Sunday showing them in the governor's office in Jalalabad, the capital of Nangarhar province.

Abrarullah Murad, a lawmaker from the province told The Associated Press (AP) that the insurgents seized Jalalabad after elders negotiated the fall of the government there. Murad said there was no fighting as the city surrendered.

The militants took also Maidan Shar, the capital of Maidan Wardak, on Sunday, only some 90 kilometers (55 miles) from Kabul, Afghan lawmaker Hamida Akbari and the Taliban said.

The fall of Mazar-e-Sharif, the country’s fourth largest city, which Afghan forces and two powerful former warlords had pledged to defend, handed on Saturday the insurgents control over all of northern Afghanistan.

Atta Mohammad Noor and Abdul Rashid Dostum, two of the warlords Ghani tried to rally to his side days earlier, fled over the border into Uzbekistan on Saturday, said officials close to Dostum. They spoke on condition of anonymity as they weren't authorized to publicly speak about his movements.

Writing on Twitter, Noor alleged a "conspiracy" aided the fall of the north to the Taliban, without elaborating.

"Despite our firm resistance, sadly, all the government and the Afghan security forces equipment were handed over to the Taliban as a result of a big organized and cowardly plot," Noor wrote. "They had orchestrated the plot to trap Marshal Dostum and myself too, but they didn’t succeed."

In his speech Saturday, Ghani vowed not to give up the "achievements" of the 20 years since the U.S.-led invasion toppled the Taliban after the 9/11 attacks.

The U.S. has continued holding peace talks between the government and the Taliban in Qatar this week, and the international community has warned that a Taliban government brought about by force would be shunned. But the insurgents appear to have little interest in making concessions as they rack up victories on the battlefield.

"We have started consultations, inside the government with elders and political leaders, representatives of different levels of the community as well as our international allies," Ghani said. "Soon the results will be shared with you," he added, without elaborating further.

Many Afghans fear a return to the Taliban’s oppressive rule. The group had previously governed Afghanistan under a harsh interpretation of religious law in which women were forbidden to work or attend school, and could not leave their homes without a male relative accompanying them.

Salima Mazari, one of the few female district governors in the country, expressed fears about a Taliban takeover Saturday in an interview from Mazar-e-Sharif, before it fell.

"There will be no place for women," said Mazari, who governs a district of 36,000 people near the northern city. "In the provinces controlled by the Taliban, no women exist there anymore, not even in the cities. They are all imprisoned in their homes."

In a statement late Saturday, however, the Taliban insisted their fighters wouldn't enter people's homes or interfere with businesses. They also said they'd offer an "amnesty" to those who worked with the Afghan government or foreign forces.

Taliban said that it "once again assures all its citizens that it will, as always, protect their life, property and honor and create a peaceful and secure environment for its beloved nation."

"In this regard, no one should worry about their life."

Despite the pledge, those who can afford a ticket have been flocking to Kabul Hamid Karzai International Airport, the only way out of the country.