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image captionThe flight will take people to Doha, the capital of Qatar
Some 200 people, including Americans, have flown out of Kabul in the first such operation since US forces left the country.
The Qatar Airways charter flight is now en route to the Qatari capital Doha, with a second flight due on Friday.
US Secretary of State Antony Blinken urged help with evacuations during a recent visit to Qatar.
Hundreds of Afghan citizens who had helped the US military were unable to get out in last month’s US airlift.
In a press conference held at the airport, Qatari special envoy Mutlaq bin Majed Al Qahtani described Kabul international airport as operational and said it was a historic day for Afghanistan.
Dutch foreign minister Sigrid Kaag has tweeted her thanks to Qatar, saying that 13 Dutch nationals were on board the flight.
The flights are the first to leave since the rushed US military-led evacuations finished last month, following the Taliban takeover of the country on 15 August.
More than 124,000 foreigners and Afghans fearful of Taliban retribution were flown out of the country.
Around 100 US citizens were thought to be left in Afghanistan before the flight.
Photos have also emerged showing injuries inflicted on two journalists who covered protests on Wednesday.
They are reported to have been badly beaten after being arrested by the Taliban in Kabul.
“One of the Taliban put his foot on my head, crushed my face against the concrete,”photographer Nematullah Naqdi told AFP news agency. “They kicked me in the head… I thought they were going to kill me.”
Mr Naqdi was covering a protest by women in front of a police station with his colleague at the local Etilaatroz newspaper, Taqi Darybai.
The Taliban have banned protests unless authorised by the justice ministry.
But dozens of demonstrators chanting “we want freedom” gathered near the Pakistan embassy in Kabul and Taliban gunmen opened fire to disperse them, protesters said.
Local media have also reported another protest by women in Kapisa province, north-east of Kabul. Sources told Aamaj news that several women had been arrested.
امروز کاپیسا – زنان با شعار اینکه «پاکستان دشمن دیرینه افغانستان است» راهپیمایی نمودند. اما منابع به آماج نیوز میگویند که این اعتراض با خشونت طالبان همراه شد و چند تن از فعالان حقوق زن بازداشت شدند.#آماج_نیوز pic.twitter.com/e0MqqPNE36
— Aamaj News (@AamajN) September 9, 2021
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BBC Dari heard from a number of Afghans about the demonstrations.
“It is our right to protest,” said Haseeneh from Kabul. “Now that we know what the Taliban meant by their new cabinet, we will protest. They kept saying that women should wait till the Taliban announce their new cabinet. There is no single woman in the cabinet.”
But Alazay from the southern province of Helmand called for other countries to recognise the Taliban government.
“If that happens, our lives are going to be much easier. If the protests continue and the Taliban suppress them, the international community will not recognise the Taliban’s new government and do you know who will suffer? We, the people.”
On Wednesday, dozens of women in Kabul and the north-eastern province of Badakhshan protested against the formation of the all-male interim Taliban government.
Some women, calling for the inclusion of female ministers in the government, were reportedly beaten before the demonstrations were broken up.
Three people were killed during a demonstration in the western city of Herat on Tuesday. The Taliban have denied that they were behind the violence.
Meanwhile, there are reports that the internet has been taken down in parts of Kabul.
Afghanistan journalist Bilal Sawary tweeted that several sources in the telecom sector had confirmed to him that the Taliban had ordered mobile phone internet coverage to be turned off temporarily in several districts.
And separately, social media footage has emerged from the Panjshir valley said to show the desecration of the mausoleum of the well-known former anti-Taliban alliance leader, Ahmed Shah Massoud.
The Taliban said on Tuesday they had taken the valley – the last region of Afghanistan holding out against their rule – from the Afghanistan National Resistance Front. The NRF, led by Ahmed Shah Massoud’s son, said they would continue to fight.