By Lauren Said-Moorhouse, Melissa Mahtani, Melissa Macaya, Maureen Chowdhury, Brad Lendon and Joshua Berlinger, CNN
A source at the Hamid Karzai international airport in Kabul has told CNN that a number of high-ranking Afghan officials, including some of President Ashraf Ghani’s advisors, arrived at the VIP lounge of the airport and were waiting for a flight out of Kabul.
Their intended destination is unknown.
Earlier Sunday an Air India flight from Delhi landed at the airport, according to flight tracking data, but an Emirates flight due to arrive from Dubai abandoned its approach.
From CNN’s Luke McGee in London
The British Parliament is being recalled from its summer recess to discuss the situation in Afghanistan, the Leader of the House of Commons Jacob Rees-Mogg told CNN on Sunday.
From CNN's Kylie Atwood
The US is completely pulling out all personnel from the embassy in Kabul over the next 72 hours, including the top officials, according to two sources familiar with the situation.
This is a rapid acceleration of the process that was only announced on Thursday. It is a situation that many State Department security officials expected would have to happen as Taliban gains accelerated in recent days.
Most of the diplomats will go to the airport in Kabul and then fly back to America.
A small number of core personnel, including the top US diplomat in the country, will remain at Kabul’s airport for now, the sources said. This means that the US embassy in Kabul will be shuttered -- at least for the time being -- by Tuesday.
The other thing to note is that US officials have repeatedly been telling CNN over the last few days that the US doesn’t have great intelligence on the ground right now. This is one of the things that is fueling the decision to get these diplomats home because they really don’t know the precise dynamics of what is happening.
One of the major reasons for this is because the United States has withdrawn most of their troops -- those who were able to collect some intelligence -- and as one US defense official put it, this makes the United States blind in the face of some potential intelligence that they used to have.
The UK is working to help its citizens and other eligible former UK staff to leave Afghanistan, said UK Home Office in a post to Twitter on Sunday as Taliban approached Kabul.
The Home Office said its officials have already resettled over 3,300 Afghan staff and their families.
From CNN’s Nick Paton Walsh in Kabul
A senior official from Afghanistan's presidential palace said the Taliban had not entered Kabul.
There had been reports of gunfire in the city, which occurred when a scuffle erupted over access to a bank and security guards and army nearby started shooting.
He said the shooting had since died down. The official pointed to the Taliban statement that they would not enter the city.
The official said that there were ongoing negotiations with a sense “of urgency” and that the president was in the palace with his national security adviser and other senior officials.
He said the Americans and Taliban were part of the “contacts” but would not specify where they were happening.
Our aim is to avoid further bloodshed and unrest in Kabul or harm to people in Kabul. Our aim is to make sure there is no violence,” the official said.
After seizing much of the country in the last several weeks, Taliban militants now surround the Afghan capital of Kabul. Carter Malkasian, a former senior adviser to the chairman of the US joint chiefs of staff, says there are a couple of reasons for the armed group's rapid advancement.
"Afghan forces, for a long period of time, have had problems with morale and also their willingness to fight the Taliban," Malkasian, who is also the author of "The American War in Afghanistan: A History," told CNN on Sunday.
"First of all, the Taliban can paint themselves as those who are resisting and fighting occupation, which is something that is kind of near and dear to what it means to be Afghan. Whereas that's a much harder thing for the government to claim, or the military forces forces fighting for the government."
He also said the Taliban's repeated successes in taking provincial cities will have impacted the confidence of Afghan security forces. "There's no doubt that morale suffers when forces face defeat after defeat," he continued.
"The more defeats that are suffered, the worst morale is going to get, so they've been suffering this kind of chain reaction for, really, the past three months. And on the other side of the fence, the Taliban are getting emboldened by success after success, and these kind of compounding effects make it even harder for the Afghan forces to hold ground."
From CNN's Tim Lister
Multiple videos from the city of Qalat, the capital of Zabul province in southeastern Afghanistan, appear to show the Taliban in control of the city, with fighters evident in the main square and the Taliban's white flag flying in several locations.
A local journalist told CNN Friday that the Taliban had entered the city.
There has been no word from the government or any provincial official on the city's status.
Twenty-five of Afghanistan's 34 provincial capitals are now held by the Taliban. The capital, Kabul, is the only city with a population of more than 100,000 still held by the government.
From CNN's Tim Lister
The embattled Afghan government is in talks with the Taliban over the country's future as the militant group surrounds the capital, Kabul.
Acting Afghan Interior Minister Abdul Sattar Mirzakwal said Sunday that Kabul will not be attacked and that they will shift power peacefully to a transitional administration, though he did not say what a transitional government may look like.
In an on-camera video statement carried by Afghan news agency TOLO, he assured Kabul residents that security forces would secure the city.
Around the same time on Sunday, the Taliban issued a statement saying it was in talks with "the opposing side" for a peaceful surrender of the capital.
Taliban spokesman Zabihullah said that all fighters had been instructed to be on standby at all entrances to Kabul until a peaceful and satisfactory transfer of power was agreed. They were also instructed about the lives, dignity and belongings of the residents of Kabul, and about not creating any danger or discomfort to them.
The security of the capital was the responsibility of the government and they should guarantee it, Zabihullah added.
From CNN's Clarissa Ward and Brent Swails in Kabul, Afghanistan
A statement issued by the Taliban on Sunday appealed for calm in the capital, Kabul, and offered assurances to its residents. It said its fighters were now closing in on the city, and wanted to seize control there "peacefully."
The statement, issued by spokesman Zabihullah Mujahid, said the group was "assuring all the banks, businesses, money exchange shops that they will be safe and protected under the Taliban and nobody would touch or bother anyone in Kabul."
"All the wealthy people, the businessmen, they should be safe and protected. None of the Taliban are allowed to go to any houses or conduct searches on businesses and the Islamic Emirate gives them full protection and they should be safe and not worry," Zabihullah said.
Tensions are running high in the capital after key cities including Jalalabad and Mazar-i-Sharif fell to the militant group overnight. Video from the city in the last 24 hours show Afghans waiting en masse at ATMs as people tried to withdraw cash, while photos show long queues at the passport office where others are trying to get their documents in order.
Zabihullah also said those who had fought against the Taliban had nothing to fear.
"The people who are trying to fight against us, we suggest to them not to do so and they will be fully protected. They can leave as ordinary people."
He continued: "We will never ask about their past or who they were and we would like to take the city peacefully. They shouldn't worry about us. We are normal people And the people who work for the Kabul government, in the military or other offices, they will all be forgiven and they’re all our brothers."